WEBVTT 00:00:00.000 --> 00:00:01.979 align:middle line:90% [SQUEAKING] 00:00:01.979 --> 00:00:03.458 align:middle line:90% [RUSTLING] 00:00:03.458 --> 00:00:06.909 align:middle line:90% [CLICKING] 00:00:06.909 --> 00:00:09.645 align:middle line:90% 00:00:09.645 --> 00:00:11.520 align:middle line:84% HAZHIR RAHMANDAD: I guess we can get started. 00:00:11.520 --> 00:00:12.700 align:middle line:90% Welcome back, folks. 00:00:12.700 --> 00:00:15.640 align:middle line:90% Good to see you all. 00:00:15.640 --> 00:00:18.340 align:middle line:84% I hope you have had a good week so far, 00:00:18.340 --> 00:00:23.560 align:middle line:84% and let's get us started today with our routine that 00:00:23.560 --> 00:00:25.540 align:middle line:84% will be repeated for the coming weeks, 00:00:25.540 --> 00:00:28.400 align:middle line:84% basically going through your models, 00:00:28.400 --> 00:00:31.560 align:middle line:84% critiquing and discussing them, and then preparing 00:00:31.560 --> 00:00:35.480 align:middle line:84% for the next session's modeling task. 00:00:35.480 --> 00:00:38.140 align:middle line:84% Before we get started, anything administrative, 00:00:38.140 --> 00:00:43.240 align:middle line:90% any questions, any issues? 00:00:43.240 --> 00:00:46.200 align:middle line:84% Everybody has access to the Dropbox folder 00:00:46.200 --> 00:00:47.540 align:middle line:90% and has been doing-- 00:00:47.540 --> 00:00:50.300 align:middle line:84% I think most of you have uploaded your models. 00:00:50.300 --> 00:00:51.640 align:middle line:90% That's great. 00:00:51.640 --> 00:00:55.080 align:middle line:84% Looking forward to working through them today. 00:00:55.080 --> 00:00:59.060 align:middle line:84% So one kind of minor point is when 00:00:59.060 --> 00:01:01.460 align:middle line:84% you're done with any file, just close it, 00:01:01.460 --> 00:01:05.080 align:middle line:84% because it creates conflicts, if, for example, 00:01:05.080 --> 00:01:09.660 align:middle line:84% I want to edit one of the-- kind of update one of the assignments 00:01:09.660 --> 00:01:11.900 align:middle line:84% because I had found some typos, if it 00:01:11.900 --> 00:01:14.180 align:middle line:84% is open in some other computer, I Can't, Or it 00:01:14.180 --> 00:01:15.320 align:middle line:90% creates multiple versions. 00:01:15.320 --> 00:01:19.420 align:middle line:84% So that's simple, but just keep that in mind 00:01:19.420 --> 00:01:23.580 align:middle line:84% because this is a shared folder with many people. 00:01:23.580 --> 00:01:27.180 align:middle line:84% So the plan for today is basically 00:01:27.180 --> 00:01:29.140 align:middle line:84% spend most of the time going through the models 00:01:29.140 --> 00:01:33.700 align:middle line:84% that you have built and then discussing them. 00:01:33.700 --> 00:01:36.060 align:middle line:84% We'll see how much material there 00:01:36.060 --> 00:01:38.460 align:middle line:84% is inside this specific exercise, 00:01:38.460 --> 00:01:41.280 align:middle line:84% because it's probably a little bit on the simpler side, 00:01:41.280 --> 00:01:45.660 align:middle line:84% and hopefully we can cover several 00:01:45.660 --> 00:01:49.460 align:middle line:84% of the submissions we have had, and we'll take it from there. 00:01:49.460 --> 00:01:56.420 align:middle line:84% So just to refresh our memories, we started with SIR model 00:01:56.420 --> 00:02:01.870 align:middle line:84% this week, and we wanted that to be expanded on a few fronts, 00:02:01.870 --> 00:02:05.470 align:middle line:84% relaxing some of the typical assumptions in SIR models. 00:02:05.470 --> 00:02:10.070 align:middle line:84% So adding a behavioral response to risk, 00:02:10.070 --> 00:02:14.790 align:middle line:84% adding the waning of immunity, thinking about equilibrium, 00:02:14.790 --> 00:02:19.430 align:middle line:84% trying to do even closed-form equilibrium 00:02:19.430 --> 00:02:23.850 align:middle line:84% to the extent possible, and then adding vaccination component. 00:02:23.850 --> 00:02:29.570 align:middle line:90% And so that was your charge. 00:02:29.570 --> 00:02:31.770 align:middle line:84% And I didn't give additional information, 00:02:31.770 --> 00:02:34.550 align:middle line:84% so you would have quite a few kind 00:02:34.550 --> 00:02:36.210 align:middle line:90% of choices you needed to make. 00:02:36.210 --> 00:02:38.970 align:middle line:84% I think those choices are things we will be discussing. 00:02:38.970 --> 00:02:40.630 align:middle line:84% And how to think about those choices 00:02:40.630 --> 00:02:42.850 align:middle line:84% more broadly is the type of lesson 00:02:42.850 --> 00:02:45.490 align:middle line:90% we hope this class helps build. 00:02:45.490 --> 00:02:50.510 align:middle line:84% So with that in mind, I have created a spreadsheet 00:02:50.510 --> 00:02:54.930 align:middle line:84% to help us just see who is going to present-- 00:02:54.930 --> 00:02:56.910 align:middle line:84% or which model we are going to work on. 00:02:56.910 --> 00:03:01.470 align:middle line:84% So I'm just showing you one so that this is a fair process. 00:03:01.470 --> 00:03:07.470 align:middle line:84% And then after that, I'll just throw the dice. 00:03:07.470 --> 00:03:09.370 align:middle line:90% So you have your names here. 00:03:09.370 --> 00:03:12.893 align:middle line:84% I look who has submitted models, add that here, 00:03:12.893 --> 00:03:14.810 align:middle line:84% so that we are only looking at the models that 00:03:14.810 --> 00:03:16.450 align:middle line:90% have been submitted. 00:03:16.450 --> 00:03:18.710 align:middle line:90% And then I draw a random number. 00:03:18.710 --> 00:03:21.870 align:middle line:84% That random number goes and selects somebody. 00:03:21.870 --> 00:03:24.410 align:middle line:84% And the probability that you get selected 00:03:24.410 --> 00:03:28.450 align:middle line:84% is partly dependent on whether you are registered officially 00:03:28.450 --> 00:03:30.290 align:middle line:90% for the class or not. 00:03:30.290 --> 00:03:32.690 align:middle line:84% So those who are registered have twice as likelihood 00:03:32.690 --> 00:03:34.430 align:middle line:84% of being selected as those who are not. 00:03:34.430 --> 00:03:38.370 align:middle line:84% And then once you're selected, I just 00:03:38.370 --> 00:03:40.830 align:middle line:84% highlight that that model is discussed. 00:03:40.830 --> 00:03:43.870 align:middle line:84% Then the next time it would not be selected. 00:03:43.870 --> 00:03:47.330 align:middle line:84% So all of that, I can now just type something 00:03:47.330 --> 00:03:51.990 align:middle line:84% and that redraws the random number, select somebody new. 00:03:51.990 --> 00:03:55.680 align:middle line:84% And I just do one random draw every time 00:03:55.680 --> 00:03:57.100 align:middle line:90% so they don't cheat anybody. 00:03:57.100 --> 00:03:57.600 align:middle line:90% OK. 00:03:57.600 --> 00:04:00.380 align:middle line:84% So the first one is Jason's model. 00:04:00.380 --> 00:04:07.180 align:middle line:84% So I'm going to put Jason's model as discussed here 00:04:07.180 --> 00:04:10.240 align:middle line:90% and take this out of your view. 00:04:10.240 --> 00:04:13.383 align:middle line:90% 00:04:13.383 --> 00:04:15.258 align:middle line:84% AUDIENCE: [INAUDIBLE] Jordan's name. 00:04:15.258 --> 00:04:16.800 align:middle line:84% HAZHIR RAHMANDAD: No, I have it here. 00:04:16.800 --> 00:04:18.399 align:middle line:90% I can just bring it up. 00:04:18.399 --> 00:04:21.120 align:middle line:84% It's probably easier than having-- 00:04:21.120 --> 00:04:23.900 align:middle line:90% 00:04:23.900 --> 00:04:24.460 align:middle line:90% OK. 00:04:24.460 --> 00:04:30.560 align:middle line:90% 00:04:30.560 --> 00:04:35.540 align:middle line:84% So this time, kind of we had three steps, so many of you 00:04:35.540 --> 00:04:37.340 align:middle line:84% have submitted three separate models, which 00:04:37.340 --> 00:04:39.660 align:middle line:84% is fine, even good, because we could 00:04:39.660 --> 00:04:42.380 align:middle line:90% go through them one by one. 00:04:42.380 --> 00:04:44.160 align:middle line:84% The models are not super complex, 00:04:44.160 --> 00:04:47.020 align:middle line:84% but it might be easier visually to start with a simpler one 00:04:47.020 --> 00:04:50.120 align:middle line:84% and just go to the next, more complex one. 00:04:50.120 --> 00:04:57.620 align:middle line:90% So let's get Vensim open. 00:04:57.620 --> 00:05:06.120 align:middle line:90% 00:05:06.120 --> 00:05:06.880 align:middle line:90% So this is-- 00:05:06.880 --> 00:05:09.100 align:middle line:84% AUDIENCE: Might need to unhide to show all levels. 00:05:09.100 --> 00:05:10.017 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:05:10.017 --> 00:05:13.399 align:middle line:90% 00:05:13.399 --> 00:05:15.020 align:middle line:90% Oh, no, not here. 00:05:15.020 --> 00:05:18.280 align:middle line:90% 00:05:18.280 --> 00:05:20.300 align:middle line:84% And for those not familiar with this feature, 00:05:20.300 --> 00:05:23.720 align:middle line:84% you can hide variables in Vensim into different layers, 00:05:23.720 --> 00:05:28.660 align:middle line:84% which kind of allows you to have simpler visualization. 00:05:28.660 --> 00:05:31.020 align:middle line:90% Let me just turn off the light. 00:05:31.020 --> 00:05:34.656 align:middle line:90% 00:05:34.656 --> 00:05:40.720 align:middle line:84% And maybe we-- is it-- no, this is too little. 00:05:40.720 --> 00:05:44.320 align:middle line:84% Is it good from the end of the room, you can see this? 00:05:44.320 --> 00:05:45.040 align:middle line:90% OK. 00:05:45.040 --> 00:05:49.610 align:middle line:84% So basic SIR model in the middle. 00:05:49.610 --> 00:05:54.290 align:middle line:84% We have death separately captured here. 00:05:54.290 --> 00:05:57.250 align:middle line:90% So that's pretty standard. 00:05:57.250 --> 00:06:02.130 align:middle line:84% And then there is the question of effective risk perception 00:06:02.130 --> 00:06:03.390 align:middle line:90% on a bunch of things. 00:06:03.390 --> 00:06:08.650 align:middle line:84% That's the first component we have been assigned. 00:06:08.650 --> 00:06:18.350 align:middle line:84% So here, we have Jason's formulation of indicated risk, 00:06:18.350 --> 00:06:23.930 align:middle line:84% if I'm reading correctly, coming from indicated infection 00:06:23.930 --> 00:06:27.290 align:middle line:90% risk and indicated death risk. 00:06:27.290 --> 00:06:30.090 align:middle line:84% We will need to go into those formulations 00:06:30.090 --> 00:06:32.170 align:middle line:90% where they come from. 00:06:32.170 --> 00:06:37.090 align:middle line:84% And then that indicated risk is leading 00:06:37.090 --> 00:06:38.735 align:middle line:90% to perceived risk somewhere. 00:06:38.735 --> 00:06:39.610 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:06:39.610 --> 00:06:41.402 align:middle line:84% HAZHIR RAHMANDAD: Ah, it's further up, yes. 00:06:41.402 --> 00:06:42.890 align:middle line:84% So then there is a smooth function 00:06:42.890 --> 00:06:46.150 align:middle line:90% that leads to risk perception. 00:06:46.150 --> 00:06:49.430 align:middle line:84% This one has two time constants consistent 00:06:49.430 --> 00:06:52.950 align:middle line:84% with an asymmetric adjustment of risk-- 00:06:52.950 --> 00:06:55.030 align:middle line:90% or risk perception. 00:06:55.030 --> 00:06:57.750 align:middle line:84% And then that perceived risk level 00:06:57.750 --> 00:07:04.470 align:middle line:84% is going to impact behaviors through impact 00:07:04.470 --> 00:07:08.010 align:middle line:84% of perceived risk on contact rate, 00:07:08.010 --> 00:07:11.650 align:middle line:84% leading to changes in contact rate. 00:07:11.650 --> 00:07:16.470 align:middle line:84% So conceptually, that's the idea. 00:07:16.470 --> 00:07:18.730 align:middle line:84% But there are a few choices here. 00:07:18.730 --> 00:07:20.770 align:middle line:84% First of all, where do you get the risk from? 00:07:20.770 --> 00:07:23.910 align:middle line:84% That is, what variables are driving the risk and risk 00:07:23.910 --> 00:07:25.030 align:middle line:90% perception? 00:07:25.030 --> 00:07:33.990 align:middle line:84% So here, we have it taken from total death. 00:07:33.990 --> 00:07:36.950 align:middle line:84% And seeing that, I'm a little bit suspicious, just 00:07:36.950 --> 00:07:40.910 align:middle line:84% because total death, for me, is the cumulative death, 00:07:40.910 --> 00:07:44.330 align:middle line:84% and therefore, itself directly shouldn't be driving it. 00:07:44.330 --> 00:07:46.360 align:middle line:84% But Jason is doing something more complex here, 00:07:46.360 --> 00:07:49.000 align:middle line:84% is the expected fractional change in death rate 00:07:49.000 --> 00:07:50.613 align:middle line:90% versus expected death rate. 00:07:50.613 --> 00:07:52.280 align:middle line:84% So we need to actually look what exactly 00:07:52.280 --> 00:07:58.420 align:middle line:84% is happening to understand whether it does the function. 00:07:58.420 --> 00:08:00.040 align:middle line:84% And then we have a similar function 00:08:00.040 --> 00:08:02.900 align:middle line:84% from infectious population in this rate. 00:08:02.900 --> 00:08:07.220 align:middle line:84% So here, you have expected death rate, 00:08:07.220 --> 00:08:14.880 align:middle line:84% which is total death multiplied by expected fractional change 00:08:14.880 --> 00:08:16.960 align:middle line:90% in death rate. 00:08:16.960 --> 00:08:22.340 align:middle line:84% So you get this expected fractional change in death rate, 00:08:22.340 --> 00:08:23.340 align:middle line:90% and you multiply that. 00:08:23.340 --> 00:08:25.360 align:middle line:90% And this is a trend function. 00:08:25.360 --> 00:08:29.760 align:middle line:84% So you are looking at the trend, and the trend 00:08:29.760 --> 00:08:33.900 align:middle line:84% is in units of unassigned unit here. 00:08:33.900 --> 00:08:36.200 align:middle line:90% So that's not good. 00:08:36.200 --> 00:08:40.320 align:middle line:84% And in fact, kind of good test at the very beginning of any-- 00:08:40.320 --> 00:08:43.260 align:middle line:90% of these is to do a unit test. 00:08:43.260 --> 00:08:47.340 align:middle line:84% 15 unit errors, that's a bad thing. 00:08:47.340 --> 00:08:49.120 align:middle line:90% You shouldn't have unit errors. 00:08:49.120 --> 00:08:51.000 align:middle line:90% That's a general rule. 00:08:51.000 --> 00:08:54.600 align:middle line:84% Never come to have a model that has unit errors. 00:08:54.600 --> 00:08:57.740 align:middle line:84% That means something might get messed up-- but OK. 00:08:57.740 --> 00:09:01.500 align:middle line:84% So fractional change in death rate-- 00:09:01.500 --> 00:09:04.460 align:middle line:84% so if I remember the trend function correctly, 00:09:04.460 --> 00:09:10.300 align:middle line:84% it is 1 over year is the unit of that function, typically. 00:09:10.300 --> 00:09:13.460 align:middle line:84% That is what is the rate of change 00:09:13.460 --> 00:09:17.200 align:middle line:84% in whatever input variable you have per unit of time. 00:09:17.200 --> 00:09:18.700 align:middle line:84% AUDIENCE: Fractional rate of change. 00:09:18.700 --> 00:09:21.075 align:middle line:84% HAZHIR RAHMANDAD: Yeah, that's fractional rate of change. 00:09:21.075 --> 00:09:28.420 align:middle line:84% So at 3%, or 0.03 means 3%, change rate in total death. 00:09:28.420 --> 00:09:32.540 align:middle line:84% You're multiplying that by expected death rate. 00:09:32.540 --> 00:09:37.120 align:middle line:84% So this, I'm not quite following the logic of that. 00:09:37.120 --> 00:09:40.565 align:middle line:84% So can you tell what you had in mind, what you wanted to do? 00:09:40.565 --> 00:09:41.190 align:middle line:90% AUDIENCE: Yeah. 00:09:41.190 --> 00:09:53.870 align:middle line:84% The idea was to think about how people might estimate 00:09:53.870 --> 00:09:57.950 align:middle line:90% the changing death rate. 00:09:57.950 --> 00:10:00.870 align:middle line:84% HAZHIR RAHMANDAD: So why do you get it from total death 00:10:00.870 --> 00:10:04.045 align:middle line:84% if you're trying to get the changing death rate? 00:10:04.045 --> 00:10:05.170 align:middle line:90% AUDIENCE: The thought was-- 00:10:05.170 --> 00:10:08.910 align:middle line:90% 00:10:08.910 --> 00:10:11.250 align:middle line:84% the goal, and I'm not sure this achieves it, 00:10:11.250 --> 00:10:15.613 align:middle line:84% was to get an estimate of the first derivative of that stock. 00:10:15.613 --> 00:10:18.030 align:middle line:84% HAZHIR RAHMANDAD: Well, the first derivative of that stock 00:10:18.030 --> 00:10:19.810 align:middle line:90% is what variable? 00:10:19.810 --> 00:10:22.050 align:middle line:90% What is the first derivative? 00:10:22.050 --> 00:10:23.110 align:middle line:90% AUDIENCE: It's the flow. 00:10:23.110 --> 00:10:24.068 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 00:10:24.068 --> 00:10:27.070 align:middle line:84% AUDIENCE: But people can't observe that. 00:10:27.070 --> 00:10:29.590 align:middle line:84% HAZHIR RAHMANDAD: So first of all, there 00:10:29.590 --> 00:10:33.690 align:middle line:84% is kind of actual measurement of death. 00:10:33.690 --> 00:10:36.550 align:middle line:84% So it is not something that is completely 00:10:36.550 --> 00:10:38.370 align:middle line:90% unobservable in the system. 00:10:38.370 --> 00:10:41.890 align:middle line:84% In fact, if there is one thing that is reasonably observed, 00:10:41.890 --> 00:10:44.230 align:middle line:90% is measures of death. 00:10:44.230 --> 00:10:46.850 align:middle line:84% Now, it is not perfect measurement. 00:10:46.850 --> 00:10:50.210 align:middle line:84% Like any measurement, it has its own delays. 00:10:50.210 --> 00:10:52.710 align:middle line:84% So the delays in measurement are important. 00:10:52.710 --> 00:10:53.830 align:middle line:90% We want to capture them. 00:10:53.830 --> 00:10:56.850 align:middle line:84% But also in a very simple model like this one, 00:10:56.850 --> 00:10:59.250 align:middle line:84% we are going to have another layer of delays 00:10:59.250 --> 00:11:01.490 align:middle line:90% from perception of risk. 00:11:01.490 --> 00:11:05.210 align:middle line:84% So I don't need to separately capture 00:11:05.210 --> 00:11:07.450 align:middle line:84% the delay in measurement, because I 00:11:07.450 --> 00:11:12.610 align:middle line:84% can say that risk perception process delays will capture not 00:11:12.610 --> 00:11:15.110 align:middle line:84% only the measurement of the death rate, 00:11:15.110 --> 00:11:19.470 align:middle line:84% but also the changes in the overall sentiment towards risk. 00:11:19.470 --> 00:11:22.370 align:middle line:84% And that will take care of the inertia in both 00:11:22.370 --> 00:11:23.950 align:middle line:90% of these measurement processes. 00:11:23.950 --> 00:11:27.170 align:middle line:84% For a simple model like this, that would be perfectly fine. 00:11:27.170 --> 00:11:28.890 align:middle line:90% Now, you may say-- 00:11:28.890 --> 00:11:31.838 align:middle line:84% you may have a model that you are trying to estimate, 00:11:31.838 --> 00:11:34.130 align:middle line:84% for example, and you would say, actually the death rate 00:11:34.130 --> 00:11:36.130 align:middle line:84% that is measured has a delay, and I 00:11:36.130 --> 00:11:37.960 align:middle line:84% want to capture that delay separately. 00:11:37.960 --> 00:11:39.020 align:middle line:90% And that's legitimate. 00:11:39.020 --> 00:11:41.860 align:middle line:84% For an estimation process, that might 00:11:41.860 --> 00:11:46.100 align:middle line:84% be an important consideration because those delays, 00:11:46.100 --> 00:11:49.438 align:middle line:84% usually in the order of days, but it might be varied. 00:11:49.438 --> 00:11:50.980 align:middle line:84% Some countries, some regions may have 00:11:50.980 --> 00:11:52.600 align:middle line:90% longer delays, shorter delays. 00:11:52.600 --> 00:11:54.820 align:middle line:84% So you may explicitly model that. 00:11:54.820 --> 00:11:56.360 align:middle line:84% AUDIENCE: Yeah, that makes sense. 00:11:56.360 --> 00:12:01.400 align:middle line:84% I did do some testing on this, and as far as I can tell, 00:12:01.400 --> 00:12:04.000 align:middle line:84% my expected death rate and expected infection rate, 00:12:04.000 --> 00:12:07.780 align:middle line:84% which is formulated equivalently, 00:12:07.780 --> 00:12:14.540 align:middle line:84% mirrored the net flows for both of those stocks quite nicely. 00:12:14.540 --> 00:12:18.060 align:middle line:84% HAZHIR RAHMANDAD: It may well be, because you are basically 00:12:18.060 --> 00:12:21.460 align:middle line:84% saying something is fractionally changing with this rate-- so 00:12:21.460 --> 00:12:23.040 align:middle line:90% 3% per rate. 00:12:23.040 --> 00:12:26.120 align:middle line:84% And then you're multiplying that by the stock, 00:12:26.120 --> 00:12:27.280 align:middle line:90% so that becomes the flow. 00:12:27.280 --> 00:12:29.700 align:middle line:84% So in that sense, you are getting the same number, 00:12:29.700 --> 00:12:34.940 align:middle line:84% but kind of going this way a little bit in the formulation. 00:12:34.940 --> 00:12:37.320 align:middle line:84% So the trend function-- yeah, the trend function 00:12:37.320 --> 00:12:40.240 align:middle line:84% is introducing kind of two, three hidden stocks 00:12:40.240 --> 00:12:42.340 align:middle line:90% inside the trend function. 00:12:42.340 --> 00:12:45.020 align:middle line:90% 00:12:45.020 --> 00:12:49.440 align:middle line:84% So we are all kind of understanding the challenges 00:12:49.440 --> 00:12:51.400 align:middle line:84% with that formulation, even though it is not 00:12:51.400 --> 00:12:53.120 align:middle line:84% wrong in the sense of conceptually 00:12:53.120 --> 00:12:55.760 align:middle line:90% it's getting to the same idea. 00:12:55.760 --> 00:12:59.400 align:middle line:84% Then there is the question of how 00:12:59.400 --> 00:13:03.240 align:middle line:84% things are happening in the aggregation of this indicated 00:13:03.240 --> 00:13:04.760 align:middle line:90% risk. 00:13:04.760 --> 00:13:07.580 align:middle line:84% So basically, you get this expected death rate. 00:13:07.580 --> 00:13:10.480 align:middle line:84% You compare with some reference death rate. 00:13:10.480 --> 00:13:13.208 align:middle line:84% And where does that reference death rate comes from? 00:13:13.208 --> 00:13:14.000 align:middle line:90% AUDIENCE: Constant. 00:13:14.000 --> 00:13:16.880 align:middle line:84% HAZHIR RAHMANDAD: It's just a constant. 00:13:16.880 --> 00:13:19.960 align:middle line:84% And you get to indicated risk, which is-- 00:13:19.960 --> 00:13:21.463 align:middle line:84% AUDIENCE: It's the sum [INAUDIBLE]. 00:13:21.463 --> 00:13:23.380 align:middle line:84% HAZHIR RAHMANDAD: --the sum of these two guys. 00:13:23.380 --> 00:13:28.520 align:middle line:90% 00:13:28.520 --> 00:13:31.180 align:middle line:84% AUDIENCE: Can I ask a question before getting into this? 00:13:31.180 --> 00:13:33.940 align:middle line:84% because the differentiating [? mechanics ?] 00:13:33.940 --> 00:13:36.300 align:middle line:84% and differentiating both the total deaths 00:13:36.300 --> 00:13:38.380 align:middle line:90% and the infected people. 00:13:38.380 --> 00:13:40.860 align:middle line:84% So my question is, are we interested 00:13:40.860 --> 00:13:44.820 align:middle line:84% in the first derivative of the infected people, 00:13:44.820 --> 00:13:48.020 align:middle line:84% because the outflow of recovery is included there 00:13:48.020 --> 00:13:49.440 align:middle line:90% when we're differentiating? 00:13:49.440 --> 00:13:49.900 align:middle line:90% AUDIENCE: Yeah, so-- 00:13:49.900 --> 00:13:51.460 align:middle line:84% AUDIENCE: Is that what we should be looking at or are we 00:13:51.460 --> 00:13:52.932 align:middle line:90% looking at infection directly? 00:13:52.932 --> 00:13:54.640 align:middle line:84% HAZHIR RAHMANDAD: What were you thinking, 00:13:54.640 --> 00:13:57.780 align:middle line:90% Jason, when you captured it? 00:13:57.780 --> 00:14:00.328 align:middle line:84% AUDIENCE: I did think about this. 00:14:00.328 --> 00:14:02.620 align:middle line:84% I'll actually walk you through my thinking [INAUDIBLE]. 00:14:02.620 --> 00:14:07.220 align:middle line:90% It's probably not sound. 00:14:07.220 --> 00:14:09.380 align:middle line:84% The first most obvious thing to me 00:14:09.380 --> 00:14:13.220 align:middle line:84% would have been to just use the death rate and infection 00:14:13.220 --> 00:14:16.020 align:middle line:90% rate for a delayed version. 00:14:16.020 --> 00:14:19.100 align:middle line:84% But in my mind, those are model variables 00:14:19.100 --> 00:14:21.700 align:middle line:90% that are not observable. 00:14:21.700 --> 00:14:23.340 align:middle line:84% They're actually driving the behavior 00:14:23.340 --> 00:14:27.380 align:middle line:84% of the system of the actual infection patterns. 00:14:27.380 --> 00:14:32.350 align:middle line:84% The behavioral cues are likely somewhat 00:14:32.350 --> 00:14:35.150 align:middle line:84% different from those true system cues. 00:14:35.150 --> 00:14:37.070 align:middle line:84% So I was thinking, OK, how would you 00:14:37.070 --> 00:14:38.730 align:middle line:90% construct the behavioral cue? 00:14:38.730 --> 00:14:42.830 align:middle line:84% And then looking in the textbook, 00:14:42.830 --> 00:14:44.770 align:middle line:90% I chose this formulation. 00:14:44.770 --> 00:14:46.150 align:middle line:90% So that was the idea. 00:14:46.150 --> 00:14:49.430 align:middle line:84% Yeah, probably not necessary to have all that machinery 00:14:49.430 --> 00:14:50.930 align:middle line:84% for what we're trying to accomplish. 00:14:50.930 --> 00:14:51.888 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 00:14:51.888 --> 00:14:54.870 align:middle line:84% So on the one hand, kind of infectious population 00:14:54.870 --> 00:14:59.390 align:middle line:84% is not any more visible than the infection rate, 00:14:59.390 --> 00:15:02.390 align:middle line:84% because infectious population is drained by a recovery that 00:15:02.390 --> 00:15:04.830 align:middle line:90% is not usually observable. 00:15:04.830 --> 00:15:11.350 align:middle line:84% So what we do have measure signals in the community-- 00:15:11.350 --> 00:15:13.690 align:middle line:84% yes, you get some signals about infection population. 00:15:13.690 --> 00:15:16.110 align:middle line:84% If your friends are sick, you know that they're sick. 00:15:16.110 --> 00:15:17.830 align:middle line:84% But also we are getting these numbers 00:15:17.830 --> 00:15:20.690 align:middle line:84% on the infection rates are not higher, 00:15:20.690 --> 00:15:23.090 align:middle line:84% we have this new number of cases, and so on. 00:15:23.090 --> 00:15:26.030 align:middle line:84% So I'm more comfortable just going with the flow 00:15:26.030 --> 00:15:27.850 align:middle line:90% variables of infection rate. 00:15:27.850 --> 00:15:30.050 align:middle line:84% Now, going back to Hesam's question, 00:15:30.050 --> 00:15:32.370 align:middle line:84% if you capture infection rate, it 00:15:32.370 --> 00:15:35.250 align:middle line:84% has a different feature characteristic 00:15:35.250 --> 00:15:38.970 align:middle line:84% than infectious population, because infectious population 00:15:38.970 --> 00:15:43.330 align:middle line:84% can actually go negative, its rate, its net flow, which 00:15:43.330 --> 00:15:46.490 align:middle line:84% means the indicated risk of infection 00:15:46.490 --> 00:15:50.170 align:middle line:84% can go negative in this formulation. 00:15:50.170 --> 00:15:54.210 align:middle line:84% And if the indicated risk of infection goes negative, 00:15:54.210 --> 00:15:57.890 align:middle line:84% then you get weird behaviors down the line, 00:15:57.890 --> 00:16:01.530 align:middle line:84% or you have to avoid those weird behaviors. 00:16:01.530 --> 00:16:05.090 align:middle line:84% That is, you need to now make sure your risk perception 00:16:05.090 --> 00:16:09.210 align:middle line:84% response doesn't respond to negative values. 00:16:09.210 --> 00:16:12.130 align:middle line:84% Now, that opens up more challenges 00:16:12.130 --> 00:16:14.510 align:middle line:84% for containing your model formulations. 00:16:14.510 --> 00:16:16.210 align:middle line:84% So I'm highlighting these because this 00:16:16.210 --> 00:16:19.490 align:middle line:84% is what is happening in my mind when I'm kind 00:16:19.490 --> 00:16:21.190 align:middle line:90% of seeing these formulations. 00:16:21.190 --> 00:16:27.260 align:middle line:84% I want you to basically build the quick simulation, mental 00:16:27.260 --> 00:16:29.500 align:middle line:84% simulation idea that you see the formulation 00:16:29.500 --> 00:16:34.620 align:middle line:84% and say, OK, but this creates additional robustness challenges 00:16:34.620 --> 00:16:37.027 align:middle line:84% down the line for me in terms of formulation. 00:16:37.027 --> 00:16:38.860 align:middle line:84% AUDIENCE: But I definitely saw that problem, 00:16:38.860 --> 00:16:43.640 align:middle line:84% and I thought about it, but didn't come to a clean answer. 00:16:43.640 --> 00:16:44.900 align:middle line:90% So it's easy to turn around. 00:16:44.900 --> 00:16:46.317 align:middle line:84% HAZHIR RAHMANDAD: No, that's fine. 00:16:46.317 --> 00:16:47.740 align:middle line:90% So actually, this is-- 00:16:47.740 --> 00:16:51.820 align:middle line:84% the purpose of this class is to actually critique and learn 00:16:51.820 --> 00:16:53.620 align:middle line:90% from those challenges. 00:16:53.620 --> 00:16:56.300 align:middle line:84% And sometimes there is a good way 00:16:56.300 --> 00:16:58.280 align:middle line:84% of thinking about it that you have applied, 00:16:58.280 --> 00:17:01.560 align:middle line:84% but the result is not necessarily the best thing. 00:17:01.560 --> 00:17:05.280 align:middle line:84% So everybody feel comfortable being critiqued here. 00:17:05.280 --> 00:17:09.020 align:middle line:90% This is the only way we learn. 00:17:09.020 --> 00:17:13.940 align:middle line:84% So that is actually probably the bigger challenge here 00:17:13.940 --> 00:17:15.780 align:middle line:84% in the indicated infection risk, just 00:17:15.780 --> 00:17:18.260 align:middle line:84% because when it goes negative, now we 00:17:18.260 --> 00:17:24.260 align:middle line:84% have a whole lot of other things like deaths are high, 00:17:24.260 --> 00:17:28.119 align:middle line:84% but the infection risk can go negative, cancel 00:17:28.119 --> 00:17:30.360 align:middle line:90% the death rate risk. 00:17:30.360 --> 00:17:34.540 align:middle line:84% So you may look at the data, and based on this formulation, 00:17:34.540 --> 00:17:38.120 align:middle line:84% sometime in January of 2022, when we had actually 00:17:38.120 --> 00:17:41.500 align:middle line:84% very high death rates and very high infection rates, 00:17:41.500 --> 00:17:44.300 align:middle line:84% you may get a risk, indicated risk, that is 0. 00:17:44.300 --> 00:17:45.260 align:middle line:90% And why is that? 00:17:45.260 --> 00:17:48.080 align:middle line:84% Because the cases are falling because the cases 00:17:48.080 --> 00:17:50.460 align:middle line:90% peak at Christmas. 00:17:50.460 --> 00:17:54.280 align:middle line:84% So the cases are now falling in mid-January. 00:17:54.280 --> 00:17:56.440 align:middle line:84% The death rates are actually very high. 00:17:56.440 --> 00:17:58.320 align:middle line:84% So at that point in time, actually 00:17:58.320 --> 00:18:00.200 align:middle line:84% the risk level, or indicated risk level, 00:18:00.200 --> 00:18:01.560 align:middle line:90% is still pretty high. 00:18:01.560 --> 00:18:03.700 align:middle line:84% It shouldn't go 0 or even negative. 00:18:03.700 --> 00:18:05.260 align:middle line:84% But the formulation doesn't get that. 00:18:05.260 --> 00:18:09.160 align:middle line:84% So that's more fundamental conceptual issue. 00:18:09.160 --> 00:18:13.120 align:middle line:84% Then there is this kind of weighing of the two risk 00:18:13.120 --> 00:18:13.900 align:middle line:90% factors. 00:18:13.900 --> 00:18:16.560 align:middle line:84% And it's OK, the way you have done it, basically, 00:18:16.560 --> 00:18:19.880 align:middle line:84% you have introduced two parameters 00:18:19.880 --> 00:18:21.940 align:middle line:90% and their values matter a lot. 00:18:21.940 --> 00:18:23.290 align:middle line:90% So this is 100. 00:18:23.290 --> 00:18:25.090 align:middle line:90% This is-- 00:18:25.090 --> 00:18:25.970 align:middle line:90% AUDIENCE: Smaller. 00:18:25.970 --> 00:18:28.012 align:middle line:84% HAZHIR RAHMANDAD: Yeah, it should be smaller one. 00:18:28.012 --> 00:18:33.970 align:middle line:84% So basically, you're saying each death gives a signal of risk 00:18:33.970 --> 00:18:38.610 align:middle line:90% that is 100 times each case. 00:18:38.610 --> 00:18:39.690 align:middle line:90% It's OK. 00:18:39.690 --> 00:18:42.450 align:middle line:84% But also, it is a little bit ad hoc. 00:18:42.450 --> 00:18:44.450 align:middle line:84% And you have introduced two degrees of freedom 00:18:44.450 --> 00:18:47.610 align:middle line:90% in the formulation that-- 00:18:47.610 --> 00:18:49.250 align:middle line:90% just more parameters. 00:18:49.250 --> 00:18:51.390 align:middle line:84% We don't want to have too many parameters. 00:18:51.390 --> 00:18:54.350 align:middle line:84% It just makes it harder for us to make sense of our model. 00:18:54.350 --> 00:18:56.810 align:middle line:84% So that would be another concern for me, 00:18:56.810 --> 00:19:00.490 align:middle line:84% that the formulations here, just we went through two parameters 00:19:00.490 --> 00:19:02.770 align:middle line:90% here for these-- 00:19:02.770 --> 00:19:06.130 align:middle line:84% for the trend function, and actually four the 00:19:06.130 --> 00:19:07.790 align:middle line:84% two-trend functions and two here. 00:19:07.790 --> 00:19:10.770 align:middle line:84% So that's now six parameters to get us 00:19:10.770 --> 00:19:14.310 align:middle line:84% to some measure of indicated risk. 00:19:14.310 --> 00:19:17.350 align:middle line:84% We do need two parameters for the time constants. 00:19:17.350 --> 00:19:18.950 align:middle line:90% So that's eight parameters. 00:19:18.950 --> 00:19:21.150 align:middle line:84% So too many degrees of freedom that 00:19:21.150 --> 00:19:23.990 align:middle line:84% makes it harder for you to analyze because you change 00:19:23.990 --> 00:19:28.390 align:middle line:84% something, but you don't know whether it's the real thing that 00:19:28.390 --> 00:19:30.610 align:middle line:90% is changing the dynamics. 00:19:30.610 --> 00:19:35.010 align:middle line:84% And then you have more parameters from the perceived-- 00:19:35.010 --> 00:19:38.190 align:middle line:84% oh, by the way, this formulation is important, 00:19:38.190 --> 00:19:41.970 align:middle line:84% and it's not as common as the standard delay. 00:19:41.970 --> 00:19:44.870 align:middle line:84% So let's take a look at it as well. 00:19:44.870 --> 00:19:49.390 align:middle line:84% So this is basically saying if the indicated risk that 00:19:49.390 --> 00:19:53.150 align:middle line:84% is the driver of that perceived value 00:19:53.150 --> 00:19:56.270 align:middle line:84% is higher than the perceived risk level, 00:19:56.270 --> 00:19:59.710 align:middle line:84% we get the indicated risk minus perceived risk divided 00:19:59.710 --> 00:20:01.790 align:middle line:90% by time to increase risk. 00:20:01.790 --> 00:20:05.230 align:middle line:84% Otherwise, it is indicated risk minus perceived risk divided 00:20:05.230 --> 00:20:07.070 align:middle line:90% by time to decrease risk. 00:20:07.070 --> 00:20:12.310 align:middle line:84% So the idea is if the actual risk level that you are-- 00:20:12.310 --> 00:20:15.510 align:middle line:84% kind of in the real world is happening is higher 00:20:15.510 --> 00:20:19.120 align:middle line:84% than your current perception of risk, you get anxious. 00:20:19.120 --> 00:20:22.640 align:middle line:84% You see more signals that things are getting worse. 00:20:22.640 --> 00:20:26.400 align:middle line:84% And people are more sensitive to these distress signals. 00:20:26.400 --> 00:20:31.120 align:middle line:84% Therefore, the time to increase risk perception 00:20:31.120 --> 00:20:33.160 align:middle line:84% is typically shorter than the time 00:20:33.160 --> 00:20:35.160 align:middle line:90% to decrease risk perception. 00:20:35.160 --> 00:20:38.280 align:middle line:84% And that asymmetry plays an important role 00:20:38.280 --> 00:20:40.660 align:middle line:84% in the dynamics of COVID, for example. 00:20:40.660 --> 00:20:44.880 align:middle line:84% And kind of people in a matter of days to weeks 00:20:44.880 --> 00:20:46.980 align:middle line:90% really start to respond. 00:20:46.980 --> 00:20:49.400 align:middle line:84% But once they are responding, it may 00:20:49.400 --> 00:20:54.760 align:middle line:84% take months to relax their responsiveness to those risks. 00:20:54.760 --> 00:20:57.100 align:middle line:90% And that plays a role. 00:20:57.100 --> 00:20:59.380 align:middle line:84% And you could empirically estimate these two, 00:20:59.380 --> 00:21:02.400 align:middle line:84% and you would see that there are actually quite different almost 00:21:02.400 --> 00:21:04.120 align:middle line:90% by an order of magnitude. 00:21:04.120 --> 00:21:06.880 align:middle line:84% So useful formulation to keep in mind 00:21:06.880 --> 00:21:09.520 align:middle line:84% when you're dealing with asymmetries in how people 00:21:09.520 --> 00:21:12.120 align:middle line:84% respond to anything, whether it is good 00:21:12.120 --> 00:21:18.360 align:middle line:84% versus bad news or risk or customer service. 00:21:18.360 --> 00:21:23.440 align:middle line:84% So customer perception of quality is very asymmetric. 00:21:23.440 --> 00:21:26.020 align:middle line:84% If you have a bad experience, it has 00:21:26.020 --> 00:21:30.260 align:middle line:84% a much stronger negative effect on your assessment than when 00:21:30.260 --> 00:21:31.800 align:middle line:90% you have a good experience. 00:21:31.800 --> 00:21:38.900 align:middle line:84% You fly, the plane lands safely, you don't get impressed. 00:21:38.900 --> 00:21:42.420 align:middle line:84% You have a bad landing, it's not going 00:21:42.420 --> 00:21:45.440 align:middle line:84% to be an experience that you will ignore. 00:21:45.440 --> 00:21:47.320 align:middle line:90% You may talk about it. 00:21:47.320 --> 00:21:49.440 align:middle line:84% You may record it and put it on TikTok. 00:21:49.440 --> 00:21:52.600 align:middle line:84% You may go and complain in a variety of networks. 00:21:52.600 --> 00:21:56.280 align:middle line:84% So that asymmetry plays a big role in organizational dynamics, 00:21:56.280 --> 00:22:00.440 align:middle line:84% in importance of keeping high levels of quality, 00:22:00.440 --> 00:22:03.160 align:middle line:84% because if you erode it, it's very hard to bring it back. 00:22:03.160 --> 00:22:04.720 align:middle line:90% It's erodes fast. 00:22:04.720 --> 00:22:06.660 align:middle line:84% Trust between people has this asymmetry. 00:22:06.660 --> 00:22:10.580 align:middle line:84% Anyway, this is generally an important conceptual thing 00:22:10.580 --> 00:22:11.560 align:middle line:90% to keep in mind. 00:22:11.560 --> 00:22:14.780 align:middle line:84% So then you have this perceived risk 00:22:14.780 --> 00:22:19.250 align:middle line:84% that feeds back into effective perceived risk on contact rate. 00:22:19.250 --> 00:22:21.050 align:middle line:90% And you have one parameter here. 00:22:21.050 --> 00:22:24.690 align:middle line:84% So this is important to take a look at this formulation. 00:22:24.690 --> 00:22:27.010 align:middle line:84% This is an important formulation. 00:22:27.010 --> 00:22:33.150 align:middle line:84% So you have 1 over e to the power of sensitivity of this-- 00:22:33.150 --> 00:22:36.250 align:middle line:84% some parameter that you have multiplied by perceived risk. 00:22:36.250 --> 00:22:38.630 align:middle line:90% So if perceived risk is a-- 00:22:38.630 --> 00:22:42.230 align:middle line:84% so for now, let's ignore the negative range 00:22:42.230 --> 00:22:45.030 align:middle line:84% for perceived risk because that negative range adds more 00:22:45.030 --> 00:22:47.890 align:middle line:90% complexity for our population. 00:22:47.890 --> 00:22:48.470 align:middle line:90% Yes? 00:22:48.470 --> 00:22:51.350 align:middle line:84% AUDIENCE: For sensitivity of CR to PR mismatch? 00:22:51.350 --> 00:22:54.330 align:middle line:84% HAZHIR RAHMANDAD: So sensitivity parameter is just a parameter. 00:22:54.330 --> 00:22:57.350 align:middle line:84% So it is controlling how responsive to risk you are. 00:22:57.350 --> 00:22:59.190 align:middle line:84% So if you assume that parameter is 00:22:59.190 --> 00:23:01.930 align:middle line:90% zero, what this function does? 00:23:01.930 --> 00:23:05.330 align:middle line:84% So when you see a function like this, 00:23:05.330 --> 00:23:07.450 align:middle line:84% you need to actually think about alternatives. 00:23:07.450 --> 00:23:09.350 align:middle line:90% And so this is one alternative. 00:23:09.350 --> 00:23:11.710 align:middle line:84% So what will happen? [? Say today, ?] if we set 00:23:11.710 --> 00:23:14.730 align:middle line:84% that sensitivity parameter to 0, what will happen 00:23:14.730 --> 00:23:16.650 align:middle line:90% to this response function? 00:23:16.650 --> 00:23:17.870 align:middle line:90% How would it behave? 00:23:17.870 --> 00:23:21.050 align:middle line:90% 00:23:21.050 --> 00:23:27.210 align:middle line:84% So this is 1 over e to the power of some parameter multiplied 00:23:27.210 --> 00:23:30.210 align:middle line:84% by some variable, perceived risk. 00:23:30.210 --> 00:23:33.690 align:middle line:84% Now we are making that parameter equal to 0. 00:23:33.690 --> 00:23:37.930 align:middle line:84% What would be the overall impact on this effect of perceived 00:23:37.930 --> 00:23:39.470 align:middle line:90% risk on contact rate? 00:23:39.470 --> 00:23:46.850 align:middle line:90% 00:23:46.850 --> 00:23:48.650 align:middle line:84% Jake, do you want to take a stab at it? 00:23:48.650 --> 00:23:50.170 align:middle line:90% AUDIENCE: Goes to 1. 00:23:50.170 --> 00:23:52.850 align:middle line:84% HAZHIR RAHMANDAD: Basically, the denominator now 00:23:52.850 --> 00:23:55.650 align:middle line:90% has e to the power of 0. 00:23:55.650 --> 00:23:57.610 align:middle line:90% e to the power of 0 is 1. 00:23:57.610 --> 00:23:59.190 align:middle line:90% So it's 1 divided by 1. 00:23:59.190 --> 00:24:00.310 align:middle line:90% So it is always 1. 00:24:00.310 --> 00:24:01.750 align:middle line:84% So it means the effect goes away. 00:24:01.750 --> 00:24:05.590 align:middle line:84% So as such, at least this extreme condition makes sense. 00:24:05.590 --> 00:24:09.330 align:middle line:84% That is, if this parameter is 0, it 00:24:09.330 --> 00:24:16.390 align:middle line:84% will put the effect at 1, which means the interaction contact 00:24:16.390 --> 00:24:19.030 align:middle line:84% rate will not change from its base value. 00:24:19.030 --> 00:24:22.850 align:middle line:84% So again, we are kind of running through a few steps, 00:24:22.850 --> 00:24:26.550 align:middle line:84% logical steps, and this kind of as you practice 00:24:26.550 --> 00:24:28.550 align:middle line:84% with these formulations, it becomes easier 00:24:28.550 --> 00:24:30.650 align:middle line:90% to digest those quickly. 00:24:30.650 --> 00:24:33.170 align:middle line:84% At the beginning, it may feel, oh, what happened? 00:24:33.170 --> 00:24:35.110 align:middle line:84% You're doing too many things mentally. 00:24:35.110 --> 00:24:36.210 align:middle line:90% You need to break it down. 00:24:36.210 --> 00:24:39.190 align:middle line:84% If it is overwhelming, write down the equation. 00:24:39.190 --> 00:24:42.070 align:middle line:84% And Vensim's lingo is not necessarily 00:24:42.070 --> 00:24:45.410 align:middle line:84% making it easier to read these things. 00:24:45.410 --> 00:24:49.750 align:middle line:84% So that extreme condition makes sense. 00:24:49.750 --> 00:24:51.590 align:middle line:84% But we also need to think about-- 00:24:51.590 --> 00:24:53.310 align:middle line:84% and the other extreme condition is 00:24:53.310 --> 00:24:57.390 align:middle line:84% if the perceived risk level 0, again, 00:24:57.390 --> 00:25:01.830 align:middle line:84% we get to a coefficient of 1, or a multiplier of 1, 00:25:01.830 --> 00:25:04.670 align:middle line:84% for effective perceived risk on contact rate, which is also 00:25:04.670 --> 00:25:08.270 align:middle line:84% meaningful, that we do want that to be the case. 00:25:08.270 --> 00:25:12.560 align:middle line:84% Now, if the perceived risk is high, 00:25:12.560 --> 00:25:15.720 align:middle line:84% multiplying that by this sensitivity parameter, and then 00:25:15.720 --> 00:25:18.960 align:middle line:84% 1 over e to the power of the sensitivity parameter. 00:25:18.960 --> 00:25:23.840 align:middle line:84% So e to the power of this number is going to be a large number. 00:25:23.840 --> 00:25:30.080 align:middle line:84% So 1 over this will be a very small number. 00:25:30.080 --> 00:25:34.440 align:middle line:84% So the idea is that this basically brings down 00:25:34.440 --> 00:25:36.120 align:middle line:90% contact rate. 00:25:36.120 --> 00:25:41.680 align:middle line:84% Again, decent, meaningful way of formulating it. 00:25:41.680 --> 00:25:43.440 align:middle line:84% Of course, you could actually just 00:25:43.440 --> 00:25:46.480 align:middle line:84% go e to the power of this sensitivity multiplied 00:25:46.480 --> 00:25:50.080 align:middle line:84% by perceived risk and make the sensitivity a negative number. 00:25:50.080 --> 00:25:53.000 align:middle line:84% Mathematically equivalent, just the functional form 00:25:53.000 --> 00:25:55.440 align:middle line:84% would look a little bit different. 00:25:55.440 --> 00:26:02.280 align:middle line:84% So this formulation works for numbers of risk, perceived risk, 00:26:02.280 --> 00:26:05.640 align:middle line:90% that are above 0. 00:26:05.640 --> 00:26:08.320 align:middle line:84% What about negative numbers for perceived risk? 00:26:08.320 --> 00:26:12.740 align:middle line:84% So if, in Jason's formulation, actually it can go negative. 00:26:12.740 --> 00:26:14.980 align:middle line:84% So if we have negative numbers, what 00:26:14.980 --> 00:26:17.540 align:middle line:90% will happen to this formulation? 00:26:17.540 --> 00:26:18.740 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:26:18.740 --> 00:26:19.440 align:middle line:90% HAZHIR RAHMANDAD: Speak up. 00:26:19.440 --> 00:26:20.898 align:middle line:84% AUDIENCE: [? It ?] [? increases. ?] 00:26:20.898 --> 00:26:25.260 align:middle line:84% HAZHIR RAHMANDAD: It goes up, the overall function 00:26:25.260 --> 00:26:27.300 align:middle line:84% because the denominator is now going 00:26:27.300 --> 00:26:33.620 align:middle line:84% to be below 1 because e to the power of a negative number 00:26:33.620 --> 00:26:34.820 align:middle line:90% is below 1. 00:26:34.820 --> 00:26:39.800 align:middle line:84% And if you have a below 1 value in the denominator, 00:26:39.800 --> 00:26:43.380 align:middle line:84% the total effect will become above 1. 00:26:43.380 --> 00:26:47.620 align:middle line:84% So it creates a large contact rate more 00:26:47.620 --> 00:26:50.140 align:middle line:90% than the normal contact rate. 00:26:50.140 --> 00:26:52.020 align:middle line:90% And do we want that? 00:26:52.020 --> 00:26:54.180 align:middle line:90% Is that realistic? 00:26:54.180 --> 00:26:55.200 align:middle line:90% It is not. 00:26:55.200 --> 00:26:59.620 align:middle line:84% So this is going to be a failure mode with the formulation 00:26:59.620 --> 00:27:03.780 align:middle line:84% that you have for the infection rate going into-- 00:27:03.780 --> 00:27:06.670 align:middle line:84% not infection rate but the change in the stock 00:27:06.670 --> 00:27:09.870 align:middle line:90% going into the formulation. 00:27:09.870 --> 00:27:12.310 align:middle line:90% Everybody clear on this? 00:27:12.310 --> 00:27:13.390 align:middle line:90% Good. 00:27:13.390 --> 00:27:21.390 align:middle line:84% So big picture, kind of in this formulation, this one 00:27:21.390 --> 00:27:23.610 align:middle line:84% I like because it has a single parameter. 00:27:23.610 --> 00:27:25.830 align:middle line:90% It does the job decently well. 00:27:25.830 --> 00:27:28.070 align:middle line:90% It's a good alternative. 00:27:28.070 --> 00:27:29.750 align:middle line:84% The only thing I would keep in mind 00:27:29.750 --> 00:27:33.270 align:middle line:84% is that exponential functions are very strong. 00:27:33.270 --> 00:27:39.470 align:middle line:84% That is, as soon as you have a perceived risk level that 00:27:39.470 --> 00:27:43.910 align:middle line:84% exceeds 1 over that sensitivity parameter, 00:27:43.910 --> 00:27:47.910 align:middle line:84% so that the multiplication of the two gets to the range of 1, 00:27:47.910 --> 00:27:54.270 align:middle line:84% this channel shuts off all of the interactions. 00:27:54.270 --> 00:27:56.990 align:middle line:84% So again, this is a little bit you 00:27:56.990 --> 00:27:59.870 align:middle line:84% need to be familiar with the exponential functions 00:27:59.870 --> 00:28:01.250 align:middle line:90% and how strong they are. 00:28:01.250 --> 00:28:03.210 align:middle line:84% But when I see the use of exponential 00:28:03.210 --> 00:28:05.850 align:middle line:84% function in this, I would ask myself, 00:28:05.850 --> 00:28:09.410 align:middle line:84% do we see such a strong change in a kind 00:28:09.410 --> 00:28:13.970 align:middle line:84% of relatively short small range of the input to the function? 00:28:13.970 --> 00:28:16.270 align:middle line:84% Because the perceived risk-- keep it in mind. 00:28:16.270 --> 00:28:21.370 align:middle line:84% This is a scaling with the size of death and cases in COVID. 00:28:21.370 --> 00:28:24.590 align:middle line:84% So in practice, you may remember in the COVID case, 00:28:24.590 --> 00:28:26.370 align:middle line:84% we had cases and deaths in the US 00:28:26.370 --> 00:28:28.350 align:middle line:84% that spanned an order of magnitude. 00:28:28.350 --> 00:28:30.370 align:middle line:84% So some days we had hundreds of deaths 00:28:30.370 --> 00:28:32.410 align:middle line:84% and some days we had thousands of deaths. 00:28:32.410 --> 00:28:37.330 align:middle line:84% So when you change an order of magnitude of input, 00:28:37.330 --> 00:28:39.650 align:middle line:84% the chances are this function will 00:28:39.650 --> 00:28:43.930 align:middle line:84% go from 1 to 0 between these two ranges. 00:28:43.930 --> 00:28:48.890 align:middle line:84% And in reality, the interactions of people in society 00:28:48.890 --> 00:28:51.890 align:middle line:84% was not changing between 0 and 1. 00:28:51.890 --> 00:28:54.770 align:middle line:84% So that's one reason I would be a little bit 00:28:54.770 --> 00:28:57.110 align:middle line:84% hesitant about the use of exponential function. 00:28:57.110 --> 00:28:58.690 align:middle line:84% On the other hand, it has the beauty 00:28:58.690 --> 00:29:04.240 align:middle line:84% of being a single parameter giving me the right range. 00:29:04.240 --> 00:29:07.160 align:middle line:84% So I'm not going to say this is a bad formulation, 00:29:07.160 --> 00:29:09.460 align:middle line:84% but I want to highlight one of its weaknesses 00:29:09.460 --> 00:29:11.600 align:middle line:90% when we are looking at this. 00:29:11.600 --> 00:29:14.740 align:middle line:90% Any thoughts, questions? 00:29:14.740 --> 00:29:16.240 align:middle line:90% OK. 00:29:16.240 --> 00:29:17.800 align:middle line:90% So this is good. 00:29:17.800 --> 00:29:21.180 align:middle line:84% Now you have the waning of immunity here 00:29:21.180 --> 00:29:26.580 align:middle line:84% that basically goes from recovered population 00:29:26.580 --> 00:29:32.520 align:middle line:84% after a delay with duration of immunity, 00:29:32.520 --> 00:29:34.360 align:middle line:84% go back to susceptible population. 00:29:34.360 --> 00:29:35.580 align:middle line:90% Very simple. 00:29:35.580 --> 00:29:39.300 align:middle line:90% This is a good approximation. 00:29:39.300 --> 00:29:42.060 align:middle line:84% People may consider whether the waning of immunity 00:29:42.060 --> 00:29:45.060 align:middle line:84% is a first-order delay or a higher-order delay. 00:29:45.060 --> 00:29:46.680 align:middle line:90% How would you think about that? 00:29:46.680 --> 00:29:50.892 align:middle line:90% 00:29:50.892 --> 00:29:52.100 align:middle line:90% AUDIENCE: I thought about it. 00:29:52.100 --> 00:29:54.460 align:middle line:84% HAZHIR RAHMANDAD: So how did you think about it? 00:29:54.460 --> 00:29:56.780 align:middle line:84% AUDIENCE: I thought it should be a higher-order delay. 00:29:56.780 --> 00:29:59.000 align:middle line:90% HAZHIR RAHMANDAD: Why? 00:29:59.000 --> 00:30:08.120 align:middle line:84% AUDIENCE: Because in the first-order formulation, 00:30:08.120 --> 00:30:12.580 align:middle line:84% you are saying that there's equal probability 00:30:12.580 --> 00:30:18.540 align:middle line:84% that any recovered person leaves the stock at any point in time. 00:30:18.540 --> 00:30:21.680 align:middle line:84% But in reality, there's some memory 00:30:21.680 --> 00:30:24.600 align:middle line:90% of when you entered the stock. 00:30:24.600 --> 00:30:30.200 align:middle line:84% If you just recovered yesterday, you probably 00:30:30.200 --> 00:30:33.725 align:middle line:84% will start losing immunity in six months from now. 00:30:33.725 --> 00:30:34.600 align:middle line:90% HAZHIR RAHMANDAD: OK. 00:30:34.600 --> 00:30:38.940 align:middle line:84% So that's an argument in favor of higher-order delays. 00:30:38.940 --> 00:30:41.560 align:middle line:84% Basically, the argument is the chances 00:30:41.560 --> 00:30:44.240 align:middle line:84% that you lose immunity overnight is very low, 00:30:44.240 --> 00:30:45.780 align:middle line:84% at least for a single individual. 00:30:45.780 --> 00:30:48.920 align:middle line:84% So if I got COVID 100 times, and I 00:30:48.920 --> 00:30:53.640 align:middle line:84% look at the distribution of my immunity loss time, 00:30:53.640 --> 00:30:57.930 align:middle line:84% it probably will not happen within the first couple 00:30:57.930 --> 00:30:59.530 align:middle line:90% of months. 00:30:59.530 --> 00:31:03.210 align:middle line:84% It starts to show off getting another COVID only 00:31:03.210 --> 00:31:06.090 align:middle line:84% after three or four months, and perhaps it 00:31:06.090 --> 00:31:08.670 align:middle line:84% peaks around five, six months or something like that. 00:31:08.670 --> 00:31:12.690 align:middle line:84% So that is the argument in favor of a higher-order delay. 00:31:12.690 --> 00:31:14.970 align:middle line:84% Any argument in favor of a lower-order delay 00:31:14.970 --> 00:31:16.810 align:middle line:90% or first-order delay? 00:31:16.810 --> 00:31:18.120 align:middle line:90% AUDIENCE: Simplicity? 00:31:18.120 --> 00:31:19.870 align:middle line:84% HAZHIR RAHMANDAD: So simplicity, for sure. 00:31:19.870 --> 00:31:22.850 align:middle line:84% So that is absolutely the main reason 00:31:22.850 --> 00:31:24.790 align:middle line:84% most of these we use first-order delays. 00:31:24.790 --> 00:31:28.730 align:middle line:84% But any other more substantive conceptual argument 00:31:28.730 --> 00:31:30.390 align:middle line:90% for a lower-order delay? 00:31:30.390 --> 00:31:35.490 align:middle line:90% 00:31:35.490 --> 00:31:38.970 align:middle line:84% AUDIENCE: I mean, [INAUDIBLE] is that we have, 00:31:38.970 --> 00:31:42.110 align:middle line:84% in this case, two first-order delays in sequence, 00:31:42.110 --> 00:31:45.010 align:middle line:84% the recovery rate and then the waning of immunity. 00:31:45.010 --> 00:31:48.410 align:middle line:90% And so like I think-- 00:31:48.410 --> 00:31:52.972 align:middle line:84% so the sum of the flows from infectious-- 00:31:52.972 --> 00:31:55.430 align:middle line:84% HAZHIR RAHMANDAD: It becomes a second-order delay of sorts. 00:31:55.430 --> 00:31:58.350 align:middle line:84% So Alexander's point is that we have the recovery 00:31:58.350 --> 00:32:02.310 align:middle line:84% rate before this delay, and that is itself a first-order delay. 00:32:02.310 --> 00:32:05.230 align:middle line:84% So the two of them together add-- 00:32:05.230 --> 00:32:07.130 align:middle line:90% create a second-order delay. 00:32:07.130 --> 00:32:10.450 align:middle line:84% So we are capturing-- so first of all, this argument, 00:32:10.450 --> 00:32:12.070 align:middle line:84% although it kind of works because it 00:32:12.070 --> 00:32:14.710 align:middle line:84% looks like a second-order delay, but it is not. 00:32:14.710 --> 00:32:16.770 align:middle line:84% This is two different delay times. 00:32:16.770 --> 00:32:19.350 align:middle line:84% So one of them is actually almost 10 times larger 00:32:19.350 --> 00:32:20.710 align:middle line:90% than the first one. 00:32:20.710 --> 00:32:23.210 align:middle line:84% So that means in practice, it behaves-- 00:32:23.210 --> 00:32:25.930 align:middle line:84% even if you had these two coupled together serially, 00:32:25.930 --> 00:32:27.970 align:middle line:84% it doesn't behave like a second-order delay. 00:32:27.970 --> 00:32:30.670 align:middle line:84% It behaves very close to a first-order delay. 00:32:30.670 --> 00:32:35.870 align:middle line:84% So the more the two or the n different time constants 00:32:35.870 --> 00:32:38.350 align:middle line:84% are similar to each other, the more 00:32:38.350 --> 00:32:40.910 align:middle line:84% it behaves like a n-th-order delay. 00:32:40.910 --> 00:32:44.990 align:middle line:84% And if they have very varied time constants, 00:32:44.990 --> 00:32:48.430 align:middle line:84% then it behaves closer to a lower-order delay. 00:32:48.430 --> 00:32:51.210 align:middle line:84% So that's good to keep in mind when you think about it. 00:32:51.210 --> 00:32:52.170 align:middle line:90% Cathy? 00:32:52.170 --> 00:32:56.360 align:middle line:84% AUDIENCE: Is it a reason why, when [? we ?] first 00:32:56.360 --> 00:32:59.000 align:middle line:84% started, because there is maybe some small segment 00:32:59.000 --> 00:33:02.640 align:middle line:84% of the population that doesn't keep their immune response 00:33:02.640 --> 00:33:03.340 align:middle line:90% for very long. 00:33:03.340 --> 00:33:04.507 align:middle line:90% HAZHIR RAHMANDAD: Very good. 00:33:04.507 --> 00:33:06.440 align:middle line:84% So that is actually a much better argument 00:33:06.440 --> 00:33:08.280 align:middle line:84% in favor of a lower-order delay, that we 00:33:08.280 --> 00:33:11.320 align:middle line:84% have a lot of heterogeneity in the population. 00:33:11.320 --> 00:33:18.320 align:middle line:84% So yes, I might map my own recovery and getting more 00:33:18.320 --> 00:33:22.200 align:middle line:84% COVID, and see even over multiple times 00:33:22.200 --> 00:33:24.260 align:middle line:84% that it never happens two months later. 00:33:24.260 --> 00:33:28.680 align:middle line:84% But there are people for whom they get repeated COVID cases 00:33:28.680 --> 00:33:31.680 align:middle line:84% every other month if they are exposed to the virus. 00:33:31.680 --> 00:33:35.360 align:middle line:84% And basically, that individual-level variation 00:33:35.360 --> 00:33:40.240 align:middle line:84% acts to make a first-order delay a decent approximation here. 00:33:40.240 --> 00:33:43.180 align:middle line:84% So that's kind of the trade-off we're talking about. 00:33:43.180 --> 00:33:47.520 align:middle line:84% Simplicity trumps for our case, which is kind of not trying 00:33:47.520 --> 00:33:49.660 align:middle line:90% to build a very detailed model. 00:33:49.660 --> 00:33:52.300 align:middle line:84% I think the first-order is a better choice just because 00:33:52.300 --> 00:33:53.080 align:middle line:90% of simplicity. 00:33:53.080 --> 00:33:55.220 align:middle line:84% But those arguments would play out 00:33:55.220 --> 00:33:59.260 align:middle line:84% if you were thinking about a more complex model-- is it worth 00:33:59.260 --> 00:33:59.780 align:middle line:90% adding that? 00:33:59.780 --> 00:34:03.380 align:middle line:84% Now, If I wanted to have a higher-order delay, how would I 00:34:03.380 --> 00:34:05.260 align:middle line:90% capture that? 00:34:05.260 --> 00:34:08.100 align:middle line:84% So then you wouldn't have the stock going 00:34:08.100 --> 00:34:10.040 align:middle line:90% into the waning of immunity. 00:34:10.040 --> 00:34:12.965 align:middle line:84% What would be the right formulation? 00:34:12.965 --> 00:34:14.340 align:middle line:84% AUDIENCE: The recovery rate would 00:34:14.340 --> 00:34:16.179 align:middle line:84% go right into the waning of immunity 00:34:16.179 --> 00:34:18.860 align:middle line:90% with the average duration. 00:34:18.860 --> 00:34:21.420 align:middle line:84% And then the difference accumulates in the stock. 00:34:21.420 --> 00:34:23.020 align:middle line:90% HAZHIR RAHMANDAD: Exactly. 00:34:23.020 --> 00:34:24.719 align:middle line:84% So that would be one way to do it. 00:34:24.719 --> 00:34:28.300 align:middle line:84% Of course, you could also spell out recovered population that 00:34:28.300 --> 00:34:31.699 align:middle line:84% have been recently recovered, recovered 00:34:31.699 --> 00:34:34.800 align:middle line:84% population that were the second cohort and third cohort. 00:34:34.800 --> 00:34:36.320 align:middle line:90% You can go to higher levels. 00:34:36.320 --> 00:34:41.300 align:middle line:84% But the simple delay function hides all of that complexity 00:34:41.300 --> 00:34:43.300 align:middle line:90% and is probably a better choice. 00:34:43.300 --> 00:34:45.860 align:middle line:84% So was that part clear for capturing 00:34:45.860 --> 00:34:47.600 align:middle line:90% the higher-order delay? 00:34:47.600 --> 00:34:49.100 align:middle line:84% AUDIENCE: [INAUDIBLE] one more time. 00:34:49.100 --> 00:34:50.270 align:middle line:90% HAZHIR RAHMANDAD: So, sure. 00:34:50.270 --> 00:34:51.290 align:middle line:90% Do ask questions. 00:34:51.290 --> 00:34:55.550 align:middle line:84% I sometimes go too fast and I'm not seeing all your faces. 00:34:55.550 --> 00:34:57.010 align:middle line:84% And even if I'm seeing your faces, 00:34:57.010 --> 00:34:59.830 align:middle line:84% I'm not reading your faces well enough. 00:34:59.830 --> 00:35:04.270 align:middle line:84% So the question was, how do we formulate a higher-order delay 00:35:04.270 --> 00:35:05.830 align:middle line:90% for waning of immunity? 00:35:05.830 --> 00:35:08.170 align:middle line:84% And the answer was there are two ways. 00:35:08.170 --> 00:35:15.270 align:middle line:84% One is to get an information link going from recovery rate 00:35:15.270 --> 00:35:17.670 align:middle line:84% all the way to waning of immunity, 00:35:17.670 --> 00:35:21.270 align:middle line:84% and then have a waning of immunity function that is 00:35:21.270 --> 00:35:25.670 align:middle line:84% a delay function that is-- or yeah, delay is the right one-- 00:35:25.670 --> 00:35:29.038 align:middle line:84% third-order delay, n-th-order delay. 00:35:29.038 --> 00:35:30.830 align:middle line:84% AUDIENCE: So you wouldn't have [INAUDIBLE]. 00:35:30.830 --> 00:35:33.830 align:middle line:84% You would just have a flow out and then directly 00:35:33.830 --> 00:35:35.810 align:middle line:84% an arrow from that flow out to another. 00:35:35.810 --> 00:35:37.150 align:middle line:90% HAZHIR RAHMANDAD: Exactly. 00:35:37.150 --> 00:35:38.110 align:middle line:90% Yes. 00:35:38.110 --> 00:35:42.290 align:middle line:84% Now, there are stocks in that formulation. 00:35:42.290 --> 00:35:44.830 align:middle line:84% So every delay function creates a stock 00:35:44.830 --> 00:35:46.870 align:middle line:84% in the back end of Vensim, but we are not 00:35:46.870 --> 00:35:49.030 align:middle line:90% observing those in our screen. 00:35:49.030 --> 00:35:51.590 align:middle line:84% So computationally, it is doing that job. 00:35:51.590 --> 00:35:53.890 align:middle line:84% It's just hiding it from your view. 00:35:53.890 --> 00:35:56.310 align:middle line:84% For better or worse, it makes things cleaner, 00:35:56.310 --> 00:35:58.410 align:middle line:84% but also you don't see the stocks that 00:35:58.410 --> 00:36:00.210 align:middle line:90% are happening in your model. 00:36:00.210 --> 00:36:03.730 align:middle line:84% The other alternative is to add explicitly 00:36:03.730 --> 00:36:06.290 align:middle line:84% multiple recovered population groups, 00:36:06.290 --> 00:36:08.730 align:middle line:84% and then have first-orders going from one 00:36:08.730 --> 00:36:12.830 align:middle line:84% to the other to the other, and that would work as well. 00:36:12.830 --> 00:36:18.570 align:middle line:84% So this model captures two of our key inclusion-- 00:36:18.570 --> 00:36:20.290 align:middle line:84% things that we wanted to consider. 00:36:20.290 --> 00:36:24.010 align:middle line:90% The third one was vaccination. 00:36:24.010 --> 00:36:25.268 align:middle line:90% Question, Alexander? 00:36:25.268 --> 00:36:26.810 align:middle line:84% AUDIENCE: Before we move on, I wanted 00:36:26.810 --> 00:36:31.690 align:middle line:84% to ask about modeling of the death rate, because I like-- 00:36:31.690 --> 00:36:36.610 align:middle line:84% so I guess my concern is that if I assume the infection fatality 00:36:36.610 --> 00:36:40.970 align:middle line:84% rate is like a hazard rate of like 0.01 per year, 00:36:40.970 --> 00:36:43.850 align:middle line:90% but if there weren't-- 00:36:43.850 --> 00:36:46.350 align:middle line:84% HAZHIR RAHMANDAD: Oh, so you are good-- you're bringing up 00:36:46.350 --> 00:36:48.010 align:middle line:90% an important problem here. 00:36:48.010 --> 00:36:54.310 align:middle line:84% So here, we have infectious population 00:36:54.310 --> 00:36:56.750 align:middle line:84% flowing to the right-hand side or flowing 00:36:56.750 --> 00:37:00.590 align:middle line:90% to the top side of the diagram. 00:37:00.590 --> 00:37:03.970 align:middle line:84% But the way they flow are through two separate parameters. 00:37:03.970 --> 00:37:05.870 align:middle line:84% One is infection fatality rate, one 00:37:05.870 --> 00:37:08.430 align:middle line:84% is the average duration of illness. 00:37:08.430 --> 00:37:12.970 align:middle line:84% Now, this is going to work mathematically, 00:37:12.970 --> 00:37:17.630 align:middle line:84% but it is going to be a problem in terms of conceptual clarity. 00:37:17.630 --> 00:37:19.270 align:middle line:90% So what is the problem? 00:37:19.270 --> 00:37:23.070 align:middle line:84% The problem is that the average duration of illness 00:37:23.070 --> 00:37:28.390 align:middle line:84% is basically capturing both people recovering 00:37:28.390 --> 00:37:31.670 align:middle line:84% and the duration for people to die. 00:37:31.670 --> 00:37:34.650 align:middle line:84% So the duration of illness, at the end of it, 00:37:34.650 --> 00:37:36.430 align:middle line:90% people either recover or die. 00:37:36.430 --> 00:37:41.270 align:middle line:84% In an extreme condition, when most of these people die, 00:37:41.270 --> 00:37:44.520 align:middle line:84% the average duration of illness is 00:37:44.520 --> 00:37:48.360 align:middle line:84% the same as in the extreme condition, but nobody dies. 00:37:48.360 --> 00:37:53.480 align:middle line:84% That is not affected by the infection fatality rate. 00:37:53.480 --> 00:37:55.600 align:middle line:84% So when you formulate it this way-- now 00:37:55.600 --> 00:37:58.360 align:middle line:84% let's go to the extreme condition in our mind 00:37:58.360 --> 00:38:03.440 align:middle line:84% that infection fatality rate, that is, if you get the disease, 00:38:03.440 --> 00:38:04.800 align:middle line:90% you will die. 00:38:04.800 --> 00:38:05.980 align:middle line:90% This is certain. 00:38:05.980 --> 00:38:08.440 align:middle line:84% This is a very sad, extreme conditions. 00:38:08.440 --> 00:38:11.880 align:middle line:84% In that situation, the flow from infectious population 00:38:11.880 --> 00:38:16.760 align:middle line:84% to recovered population should be 0. 00:38:16.760 --> 00:38:21.400 align:middle line:84% But in Jason's formulation, that will not happen automatically. 00:38:21.400 --> 00:38:24.800 align:middle line:84% Now, of course, Jason can redefine average duration 00:38:24.800 --> 00:38:28.480 align:middle line:84% of illness to combine the probability that you survive 00:38:28.480 --> 00:38:30.380 align:middle line:90% and the duration of illness. 00:38:30.380 --> 00:38:33.260 align:middle line:84% But that is a convoluted way of defining your parameters, 00:38:33.260 --> 00:38:36.040 align:middle line:84% because now you can't fix that parameter based 00:38:36.040 --> 00:38:38.220 align:middle line:84% on biological knowledge you have. 00:38:38.220 --> 00:38:41.260 align:middle line:84% You have to play with these things in your head, 00:38:41.260 --> 00:38:43.160 align:middle line:90% and so you don't want that. 00:38:43.160 --> 00:38:45.280 align:middle line:84% So what's the right way of formulating this? 00:38:45.280 --> 00:38:48.940 align:middle line:84% So basically, what you need is to split the total population 00:38:48.940 --> 00:38:52.540 align:middle line:84% that gets to the gate of recovery or death 00:38:52.540 --> 00:38:55.460 align:middle line:84% and split it between these two channels. 00:38:55.460 --> 00:38:58.180 align:middle line:90% So what's the right formulation? 00:38:58.180 --> 00:39:01.145 align:middle line:84% Do you have a solution yourself, Jason? 00:39:01.145 --> 00:39:03.020 align:middle line:84% AUDIENCE: Could use some type of [INAUDIBLE], 00:39:03.020 --> 00:39:05.125 align:middle line:90% like a fractional allocation. 00:39:05.125 --> 00:39:07.000 align:middle line:84% HAZHIR RAHMANDAD: So what would it look like? 00:39:07.000 --> 00:39:16.220 align:middle line:90% 00:39:16.220 --> 00:39:17.950 align:middle line:84% AUDIENCE: You could have fraction of-- 00:39:17.950 --> 00:39:18.700 align:middle line:90% OK. [? Hang ?] on. 00:39:18.700 --> 00:39:20.320 align:middle line:90% I have to think on my feet. 00:39:20.320 --> 00:39:26.900 align:middle line:90% 00:39:26.900 --> 00:39:29.220 align:middle line:84% AUDIENCE: Well, you could have a separate-- you 00:39:29.220 --> 00:39:30.520 align:middle line:90% could introduce another stock. 00:39:30.520 --> 00:39:31.937 align:middle line:84% AUDIENCE: I'm hesitant to do that. 00:39:31.937 --> 00:39:34.780 align:middle line:84% HAZHIR RAHMANDAD: Definitely don't do that. 00:39:34.780 --> 00:39:36.380 align:middle line:90% You don't need a stock. 00:39:36.380 --> 00:39:39.226 align:middle line:90% AUDIENCE: So fraction-- 00:39:39.226 --> 00:39:43.530 align:middle line:90% 00:39:43.530 --> 00:39:46.190 align:middle line:84% HAZHIR RAHMANDAD: So what's the total number of people getting 00:39:46.190 --> 00:39:48.030 align:middle line:90% out of the infectious stock? 00:39:48.030 --> 00:39:49.890 align:middle line:84% The stock of infectious population. 00:39:49.890 --> 00:39:52.630 align:middle line:84% AUDIENCE: It's the sum of death rate and recovery rate. 00:39:52.630 --> 00:39:54.422 align:middle line:84% HAZHIR RAHMANDAD: Yes, in this formulation. 00:39:54.422 --> 00:39:56.590 align:middle line:84% But if you have a total recovery time, 00:39:56.590 --> 00:39:59.030 align:middle line:90% average duration of illness-- 00:39:59.030 --> 00:40:01.590 align:middle line:84% not recovery time, average duration of illness. 00:40:01.590 --> 00:40:05.650 align:middle line:84% So you wanted to calculate the total exit from this stock, 00:40:05.650 --> 00:40:11.070 align:middle line:84% what would it be from the stock of infectious? 00:40:11.070 --> 00:40:14.510 align:middle line:84% AUDIENCE: It would be the duration times the infection 00:40:14.510 --> 00:40:16.403 align:middle line:90% rate in equilibrium. 00:40:16.403 --> 00:40:18.570 align:middle line:84% HAZHIR RAHMANDAD: I'm not talking about equilibrium. 00:40:18.570 --> 00:40:21.350 align:middle line:84% I'm talking about just you are trying 00:40:21.350 --> 00:40:23.850 align:middle line:84% to drain a stock with an average duration. 00:40:23.850 --> 00:40:26.470 align:middle line:90% What would the outflow be? 00:40:26.470 --> 00:40:28.230 align:middle line:84% AUDIENCE: Oh, just a first-order-- 00:40:28.230 --> 00:40:29.150 align:middle line:84% HAZHIR RAHMANDAD: Yeah, just the stock 00:40:29.150 --> 00:40:30.275 align:middle line:90% divided by the [INAUDIBLE]. 00:40:30.275 --> 00:40:33.550 align:middle line:84% So that's the total that should get out of the stock. 00:40:33.550 --> 00:40:38.103 align:middle line:84% Now you need to split that total between these two channels. 00:40:38.103 --> 00:40:38.770 align:middle line:90% AUDIENCE: I see. 00:40:38.770 --> 00:40:40.570 align:middle line:84% HAZHIR RAHMANDAD: So you get that total, 00:40:40.570 --> 00:40:45.570 align:middle line:84% you multiply that number with infection fatality rate, which 00:40:45.570 --> 00:40:48.370 align:middle line:84% is what fraction of people die from disease 00:40:48.370 --> 00:40:49.810 align:middle line:90% if they got the disease. 00:40:49.810 --> 00:40:52.410 align:middle line:84% And that goes up to the death rate. 00:40:52.410 --> 00:40:56.408 align:middle line:84% And 1 minus that fraction goes down to the recovery rate. 00:40:56.408 --> 00:40:57.950 align:middle line:84% AUDIENCE: Just to say it another way, 00:40:57.950 --> 00:41:01.090 align:middle line:84% it's a question of when the splitting happens. 00:41:01.090 --> 00:41:04.588 align:middle line:90% HAZHIR RAHMANDAD: Well, yes. 00:41:04.588 --> 00:41:06.130 align:middle line:84% In that sense, you could call it also 00:41:06.130 --> 00:41:08.330 align:middle line:84% about when a splitting happens, but it is really 00:41:08.330 --> 00:41:12.010 align:middle line:84% kind of separating these two parameters of infection fatality 00:41:12.010 --> 00:41:15.010 align:middle line:84% rate versus average duration of illness from each other 00:41:15.010 --> 00:41:16.618 align:middle line:90% so that they don't convolute. 00:41:16.618 --> 00:41:17.910 align:middle line:90% Right now, they are convoluted. 00:41:17.910 --> 00:41:19.730 align:middle line:90% You're calling them the-- 00:41:19.730 --> 00:41:21.950 align:middle line:84% something, but they're actually different things. 00:41:21.950 --> 00:41:23.890 align:middle line:84% So the one that is going to the top right now 00:41:23.890 --> 00:41:26.010 align:middle line:84% is infection fatality rate multiplied 00:41:26.010 --> 00:41:27.870 align:middle line:90% by average duration of illness. 00:41:27.870 --> 00:41:31.770 align:middle line:84% The one that is going down is 1 minus infection fatality 00:41:31.770 --> 00:41:34.150 align:middle line:84% rate multiplied by average duration of illness. 00:41:34.150 --> 00:41:38.160 align:middle line:84% That's not a good way of doing the formulation. 00:41:38.160 --> 00:41:40.645 align:middle line:84% AUDIENCE: Duration to determine the flow and then-- 00:41:40.645 --> 00:41:42.020 align:middle line:84% HAZHIR RAHMANDAD: The total flow. 00:41:42.020 --> 00:41:44.000 align:middle line:84% And then fractional goes to the two. 00:41:44.000 --> 00:41:44.965 align:middle line:90% AUDIENCE: Makes sense. 00:41:44.965 --> 00:41:46.340 align:middle line:84% HAZHIR RAHMANDAD: Yes, Alexander? 00:41:46.340 --> 00:41:48.060 align:middle line:84% AUDIENCE: So that kind of implicitly 00:41:48.060 --> 00:41:50.863 align:middle line:84% assumes that it takes the same time to die from a disease 00:41:50.863 --> 00:41:51.780 align:middle line:90% as to recover from it? 00:41:51.780 --> 00:41:52.460 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:41:52.460 --> 00:41:53.070 align:middle line:90% Absolutely. 00:41:53.070 --> 00:41:55.320 align:middle line:84% AUDIENCE: So if there's a disease where if you get it, 00:41:55.320 --> 00:41:58.020 align:middle line:84% you'll die within the first week, otherwise you're-- 00:41:58.020 --> 00:41:59.180 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:41:59.180 --> 00:42:05.380 align:middle line:84% So this is kind of a first-order approximation for that idea. 00:42:05.380 --> 00:42:07.140 align:middle line:84% If you want to break it down, then you 00:42:07.140 --> 00:42:10.360 align:middle line:84% need to break down into different stages of the disease. 00:42:10.360 --> 00:42:14.340 align:middle line:84% So rather than have a single stock of infectious population, 00:42:14.340 --> 00:42:17.780 align:middle line:84% you would need kind of people with early disease and later 00:42:17.780 --> 00:42:20.520 align:middle line:84% stage and second week or third week or whatever you think. 00:42:20.520 --> 00:42:22.220 align:middle line:84% And then you would have different rates 00:42:22.220 --> 00:42:23.320 align:middle line:90% of death for them. 00:42:23.320 --> 00:42:24.780 align:middle line:90% But it is a messy formulation. 00:42:24.780 --> 00:42:26.920 align:middle line:84% When you get to go down that route, 00:42:26.920 --> 00:42:30.200 align:middle line:84% you can't have a single infection fatality rate. 00:42:30.200 --> 00:42:34.840 align:middle line:84% Now you have to have stage-based infection fatality rates that 00:42:34.840 --> 00:42:35.720 align:middle line:90% kind of-- 00:42:35.720 --> 00:42:38.200 align:middle line:84% it's doable, but you will introduce 00:42:38.200 --> 00:42:42.120 align:middle line:84% more degrees of freedom and more places for confusion. 00:42:42.120 --> 00:42:44.560 align:middle line:84% AUDIENCE: Another way-- I'm hammering this one because I 00:42:44.560 --> 00:42:47.020 align:middle line:84% had an issue with during [INAUDIBLE] sense 00:42:47.020 --> 00:42:48.880 align:middle line:90% of drug tests failing. 00:42:48.880 --> 00:42:50.642 align:middle line:84% [INAUDIBLE] moving on and [INAUDIBLE]. 00:42:50.642 --> 00:42:51.600 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 00:42:51.600 --> 00:42:54.160 align:middle line:84% AUDIENCE: So what another way to do this be you 00:42:54.160 --> 00:42:57.200 align:middle line:84% have say like two socks, and then you 00:42:57.200 --> 00:42:59.240 align:middle line:84% split them in the [? influence. ?] 00:42:59.240 --> 00:43:02.300 align:middle line:84% Then you have infections going into both. 00:43:02.300 --> 00:43:04.240 align:middle line:84% And then some proportion of the infections 00:43:04.240 --> 00:43:06.500 align:middle line:84% are like destined to die, so to speak. 00:43:06.500 --> 00:43:10.640 align:middle line:84% And then they go into infecteds who will die, 00:43:10.640 --> 00:43:14.040 align:middle line:84% and then they flow out using their own [INAUDIBLE] rate 00:43:14.040 --> 00:43:15.220 align:middle line:90% like time constant. 00:43:15.220 --> 00:43:17.880 align:middle line:84% And then infecteds who will recover and they flow out-- 00:43:17.880 --> 00:43:19.422 align:middle line:84% HAZHIR RAHMANDAD: So you're basically 00:43:19.422 --> 00:43:22.960 align:middle line:84% imagining two parallel stock and flow chains 00:43:22.960 --> 00:43:24.480 align:middle line:84% for people who are destined to die 00:43:24.480 --> 00:43:27.800 align:middle line:84% and people who are destined to survive? 00:43:27.800 --> 00:43:29.440 align:middle line:84% You can do it that way, but then you're 00:43:29.440 --> 00:43:31.410 align:middle line:90% introducing even more stocks. 00:43:31.410 --> 00:43:33.810 align:middle line:84% So the nice thing about that option 00:43:33.810 --> 00:43:36.850 align:middle line:84% is that from the very beginning, you use your infection fatality 00:43:36.850 --> 00:43:40.690 align:middle line:84% rate to divide people between these two chains. 00:43:40.690 --> 00:43:43.050 align:middle line:84% And then you are just doing the timing 00:43:43.050 --> 00:43:46.570 align:middle line:84% thing, that timing of recovery versus timing of death. 00:43:46.570 --> 00:43:50.650 align:middle line:84% The downside of it is now you have extra stocks 00:43:50.650 --> 00:43:53.890 align:middle line:84% that you're tracking, rather than tracking 00:43:53.890 --> 00:43:57.750 align:middle line:84% all of the people in the same stock. 00:43:57.750 --> 00:44:00.810 align:middle line:90% 00:44:00.810 --> 00:44:02.070 align:middle line:90% You can do both of them. 00:44:02.070 --> 00:44:05.750 align:middle line:84% Really depends on what you have data for. 00:44:05.750 --> 00:44:08.870 align:middle line:84% So if you have data and first week, 00:44:08.870 --> 00:44:14.210 align:middle line:84% what is your risk of death versus risk of survival, 00:44:14.210 --> 00:44:16.970 align:middle line:84% then you can use the single stock chain. 00:44:16.970 --> 00:44:19.990 align:middle line:84% If you have only total infection fatality rate, 00:44:19.990 --> 00:44:22.330 align:middle line:84% then maybe it is worth separating them. 00:44:22.330 --> 00:44:24.250 align:middle line:84% Now, for this problem, i wouldn't even 00:44:24.250 --> 00:44:27.650 align:middle line:84% think about any of these, but for the general case. 00:44:27.650 --> 00:44:30.167 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:44:30.167 --> 00:44:32.250 align:middle line:84% HAZHIR RAHMANDAD: Could you speak up a little bit? 00:44:32.250 --> 00:44:34.570 align:middle line:84% I just want to make sure folks online can hear us? 00:44:34.570 --> 00:44:37.990 align:middle line:84% AUDIENCE: So it's wrong to have the average duration of illness, 00:44:37.990 --> 00:44:40.470 align:middle line:84% for example, seven days, and then 00:44:40.470 --> 00:44:43.530 align:middle line:84% have average duration of illness that leads to death, 00:44:43.530 --> 00:44:45.350 align:middle line:90% let's say, 21 days. 00:44:45.350 --> 00:44:47.615 align:middle line:84% Even if you have the fraction allocated? 00:44:47.615 --> 00:44:48.490 align:middle line:90% HAZHIR RAHMANDAD: No. 00:44:48.490 --> 00:44:51.190 align:middle line:84% So if you want to do that, then you're dealing with the problem 00:44:51.190 --> 00:44:52.890 align:middle line:90% that Alexander is talking about. 00:44:52.890 --> 00:44:56.670 align:middle line:84% That is, then you probably benefit from splitting them 00:44:56.670 --> 00:44:59.170 align:middle line:90% earlier into two groups. 00:44:59.170 --> 00:45:01.470 align:middle line:84% The people who are destined to die. 00:45:01.470 --> 00:45:03.950 align:middle line:84% You put them into that stock, and after 21 days, 00:45:03.950 --> 00:45:05.070 align:middle line:90% you kill them. 00:45:05.070 --> 00:45:08.730 align:middle line:84% The people who are going to survive after seven, 00:45:08.730 --> 00:45:11.590 align:middle line:84% then you take them out and put them 00:45:11.590 --> 00:45:14.630 align:middle line:90% into the recovered population. 00:45:14.630 --> 00:45:18.950 align:middle line:84% AUDIENCE: Well, can you explain why it's wrong to do that? 00:45:18.950 --> 00:45:21.110 align:middle line:84% HAZHIR RAHMANDAD: So it's not wrong. 00:45:21.110 --> 00:45:26.150 align:middle line:84% It is just now you have two different types of people, 00:45:26.150 --> 00:45:31.120 align:middle line:84% people who spend in the kind of sickness stage for 21 days, 00:45:31.120 --> 00:45:34.840 align:middle line:84% and people who stay in the sickness stage for seven days. 00:45:34.840 --> 00:45:40.040 align:middle line:84% And if you really want to track this distinction, 00:45:40.040 --> 00:45:43.600 align:middle line:84% you would need at least two different stocks. 00:45:43.600 --> 00:45:48.160 align:middle line:84% Now, you could have those two different stocks either serially 00:45:48.160 --> 00:45:49.840 align:middle line:90% or in parallel. 00:45:49.840 --> 00:45:54.340 align:middle line:84% So if you did it serially, you would say, OK, I have a group-- 00:45:54.340 --> 00:45:56.040 align:middle line:90% I have the first stock. 00:45:56.040 --> 00:45:58.120 align:middle line:84% After seven days, people leave this stock, 00:45:58.120 --> 00:46:02.020 align:middle line:84% and most people leave that stock after seven days. 00:46:02.020 --> 00:46:05.340 align:middle line:84% But then a small chunk of people go to the second stage, 00:46:05.340 --> 00:46:06.800 align:middle line:90% which is the stage of-- 00:46:06.800 --> 00:46:09.840 align:middle line:84% I don't know-- being condemned to death. 00:46:09.840 --> 00:46:12.700 align:middle line:84% And they will stay there for 14 days, 00:46:12.700 --> 00:46:15.960 align:middle line:84% and at the end of that period, they would die. 00:46:15.960 --> 00:46:17.922 align:middle line:84% So that's the alternative way of capturing it. 00:46:17.922 --> 00:46:19.880 align:middle line:84% But it is a little bit of a more convoluted way 00:46:19.880 --> 00:46:23.040 align:middle line:84% of doing it, because then that is splitting going down 00:46:23.040 --> 00:46:24.260 align:middle line:90% versus going up. 00:46:24.260 --> 00:46:28.780 align:middle line:84% You need to do some calculation, what is the exact fraction that 00:46:28.780 --> 00:46:30.900 align:middle line:90% goes versus stays? 00:46:30.900 --> 00:46:33.320 align:middle line:84% That's not obvious at the beginning, 00:46:33.320 --> 00:46:36.860 align:middle line:84% although it is-- basically ends up to be your infection fatality 00:46:36.860 --> 00:46:39.120 align:middle line:90% rate for that split. 00:46:39.120 --> 00:46:40.685 align:middle line:84% So you can do it that way as well. 00:46:40.685 --> 00:46:42.060 align:middle line:84% AUDIENCE: So, basically, here you 00:46:42.060 --> 00:46:45.580 align:middle line:84% would have the average duration of illness being 00:46:45.580 --> 00:46:47.440 align:middle line:90% the same as for the people-- 00:46:47.440 --> 00:46:50.060 align:middle line:84% HAZHIR RAHMANDAD: So this is not happening, 00:46:50.060 --> 00:46:51.680 align:middle line:90% not in Jason's formulation. 00:46:51.680 --> 00:46:54.220 align:middle line:84% Jason's formulation is just problematic. 00:46:54.220 --> 00:46:57.220 align:middle line:84% So the meaning of average duration 00:46:57.220 --> 00:46:58.900 align:middle line:84% of illness and infection fatality rate 00:46:58.900 --> 00:47:01.142 align:middle line:84% are just not correctly captured here. 00:47:01.142 --> 00:47:02.600 align:middle line:84% And therefore, in this formulation, 00:47:02.600 --> 00:47:04.380 align:middle line:90% it is doing some weird thing. 00:47:04.380 --> 00:47:07.440 align:middle line:84% We are not going to belabor that point. 00:47:07.440 --> 00:47:09.720 align:middle line:84% But in the right way of doing it, 00:47:09.720 --> 00:47:12.700 align:middle line:84% you would have an average duration of illness that 00:47:12.700 --> 00:47:15.660 align:middle line:90% affects both of these flows. 00:47:15.660 --> 00:47:18.220 align:middle line:84% And then that would be the average time people 00:47:18.220 --> 00:47:20.783 align:middle line:84% stay in the infectious population stock. 00:47:20.783 --> 00:47:21.700 align:middle line:90% AUDIENCE: Makes sense. 00:47:21.700 --> 00:47:23.200 align:middle line:90% HAZHIR RAHMANDAD: OK. 00:47:23.200 --> 00:47:27.760 align:middle line:84% So I think we kind of critiqued this model well enough. 00:47:27.760 --> 00:47:30.880 align:middle line:84% The biggest lesson, always be unit 00:47:30.880 --> 00:47:35.620 align:middle line:84% consistent before putting your model up. 00:47:35.620 --> 00:47:40.880 align:middle line:84% So let's do the next part, the vaccination on some other model, 00:47:40.880 --> 00:47:44.320 align:middle line:84% just to have a little bit of variance. 00:47:44.320 --> 00:47:52.720 align:middle line:90% 00:47:52.720 --> 00:47:55.500 align:middle line:90% So this time we have Russ. 00:47:55.500 --> 00:47:59.160 align:middle line:90% 00:47:59.160 --> 00:48:00.920 align:middle line:90% OK. 00:48:00.920 --> 00:48:08.420 align:middle line:90% Let me open Russ's model. 00:48:08.420 --> 00:48:19.700 align:middle line:84% So let's actually just get our bearing around this diagram. 00:48:19.700 --> 00:48:21.570 align:middle line:90% Let's see. 00:48:21.570 --> 00:48:28.690 align:middle line:84% So we have unvaccinated population and their movement 00:48:28.690 --> 00:48:37.790 align:middle line:84% between susceptible, recovered, and infected. 00:48:37.790 --> 00:48:40.130 align:middle line:84% So this is the three stocks we have 00:48:40.130 --> 00:48:45.330 align:middle line:84% in the center are the stocks we already saw in Jason's model. 00:48:45.330 --> 00:48:47.670 align:middle line:84% And then we have the vaccination process. 00:48:47.670 --> 00:48:51.490 align:middle line:84% So people get vaccinated, they go into vaccinated populations 00:48:51.490 --> 00:48:53.130 align:middle line:90% susceptible to COVID. 00:48:53.130 --> 00:48:54.230 align:middle line:90% They may get COVID. 00:48:54.230 --> 00:49:00.730 align:middle line:84% So you have basically the three equivalent parts-- 00:49:00.730 --> 00:49:05.050 align:middle line:84% three equivalent stocks on the left-hand side. 00:49:05.050 --> 00:49:07.770 align:middle line:90% So, conceptually same idea. 00:49:07.770 --> 00:49:11.930 align:middle line:84% I would probably just make them parallel on the top or bottom 00:49:11.930 --> 00:49:14.530 align:middle line:84% so that it is a little bit visually easier to see 00:49:14.530 --> 00:49:18.010 align:middle line:84% the parallelism between the two, but there is nothing conceptual 00:49:18.010 --> 00:49:20.750 align:middle line:90% there. 00:49:20.750 --> 00:49:23.190 align:middle line:84% Let's now-- just so that I quickly 00:49:23.190 --> 00:49:27.710 align:middle line:84% understand what Russ's model is doing, 00:49:27.710 --> 00:49:30.630 align:middle line:84% we have the risk perception, and then 00:49:30.630 --> 00:49:39.390 align:middle line:84% we have the impact of risk perception on contact rate 00:49:39.390 --> 00:49:42.710 align:middle line:90% or on infection rate. 00:49:42.710 --> 00:49:49.750 align:middle line:84% And that process is contact rate multiplied 00:49:49.750 --> 00:49:53.910 align:middle line:84% by infectivity multiplied by unvaccinated population 00:49:53.910 --> 00:49:57.750 align:middle line:84% susceptible to COVID multiplied by population infected 00:49:57.750 --> 00:50:01.750 align:middle line:84% with COVID divided by total population multiplied 00:50:01.750 --> 00:50:03.710 align:middle line:90% by 1 minus perceived risk. 00:50:03.710 --> 00:50:08.530 align:middle line:84% So what are the challenges you see with this formulation? 00:50:08.530 --> 00:50:13.630 align:middle line:84% So any things that come to your mind looking at this formulation 00:50:13.630 --> 00:50:15.358 align:middle line:90% quickly? 00:50:15.358 --> 00:50:17.230 align:middle line:90% AUDIENCE: The range [INAUDIBLE]? 00:50:17.230 --> 00:50:18.980 align:middle line:84% HAZHIR RAHMANDAD: Can you speak up, Hesam? 00:50:18.980 --> 00:50:21.220 align:middle line:84% AUDIENCE: What is the range for perceived risk in this model? 00:50:21.220 --> 00:50:22.762 align:middle line:84% HAZHIR RAHMANDAD: Very good question. 00:50:22.762 --> 00:50:26.440 align:middle line:84% So the range for perceived risk matters a lot here, 00:50:26.440 --> 00:50:29.580 align:middle line:84% because if it is 1 minus some number, 00:50:29.580 --> 00:50:32.560 align:middle line:84% if the perceived risk is large enough, what will 00:50:32.560 --> 00:50:34.620 align:middle line:90% happen to this 1 minus thing? 00:50:34.620 --> 00:50:35.840 align:middle line:90% It goes negative. 00:50:35.840 --> 00:50:38.070 align:middle line:84% Now you will have negative infection rate, 00:50:38.070 --> 00:50:38.820 align:middle line:90% which is terrible. 00:50:38.820 --> 00:50:41.280 align:middle line:84% It will just mess up all of your model. 00:50:41.280 --> 00:50:43.400 align:middle line:84% So I haven't looked at your perceived risk 00:50:43.400 --> 00:50:44.780 align:middle line:90% formulation, Russ. 00:50:44.780 --> 00:50:47.620 align:middle line:84% It might be already captured in the perceived risk part. 00:50:47.620 --> 00:50:51.720 align:middle line:84% So we shouldn't judge it yet too fast. 00:50:51.720 --> 00:50:53.280 align:middle line:90% So we'll look at that. 00:50:53.280 --> 00:50:56.920 align:middle line:84% The other part that I'm concerned about this 00:50:56.920 --> 00:51:01.680 align:middle line:84% is population infected with COVID here. 00:51:01.680 --> 00:51:03.800 align:middle line:90% Why am I worried about that? 00:51:03.800 --> 00:51:04.900 align:middle line:90% Anybody can tell? 00:51:04.900 --> 00:51:08.140 align:middle line:84% So this is very standard SIR model. 00:51:08.140 --> 00:51:10.720 align:middle line:84% So you have the total infection rate 00:51:10.720 --> 00:51:15.120 align:middle line:84% is infected fraction of population multiplied 00:51:15.120 --> 00:51:21.220 align:middle line:84% by the susceptible multiplied by some contact and infectivity. 00:51:21.220 --> 00:51:23.120 align:middle line:90% So what could go wrong here? 00:51:23.120 --> 00:51:31.540 align:middle line:90% 00:51:31.540 --> 00:51:32.540 align:middle line:90% AUDIENCE: [INAUDIBLE] 00:51:32.540 --> 00:51:33.498 align:middle line:90% HAZHIR RAHMANDAD: Jake. 00:51:33.498 --> 00:51:34.860 align:middle line:90% AUDIENCE: I mean, one thing is-- 00:51:34.860 --> 00:51:36.480 align:middle line:84% I don't know if this is the thing you're talking about, 00:51:36.480 --> 00:51:39.020 align:middle line:84% but one thing is I think this is a separate-- like he also 00:51:39.020 --> 00:51:41.633 align:middle line:84% has a separate stock for vaccinated population. 00:51:41.633 --> 00:51:42.800 align:middle line:90% HAZHIR RAHMANDAD: Very good. 00:51:42.800 --> 00:51:45.380 align:middle line:84% So the vaccinated population who are infected 00:51:45.380 --> 00:51:46.880 align:middle line:90% are missing from this equation. 00:51:46.880 --> 00:51:49.220 align:middle line:84% And those people can also infect people. 00:51:49.220 --> 00:51:53.740 align:middle line:84% So you need to actually include the vaccinated population that 00:51:53.740 --> 00:51:57.020 align:middle line:84% is infected, otherwise the accounting will be all messed 00:51:57.020 --> 00:51:58.140 align:middle line:90% up. 00:51:58.140 --> 00:52:02.060 align:middle line:84% Now, if you want to include the vaccinated population that 00:52:02.060 --> 00:52:06.060 align:middle line:84% are infected into your calculation of infection rate, 00:52:06.060 --> 00:52:08.420 align:middle line:84% so the first-order way of doing it is just 00:52:08.420 --> 00:52:11.900 align:middle line:84% add that population infected with COVID 00:52:11.900 --> 00:52:15.610 align:middle line:84% plus vaccinated population infected with COVID, 00:52:15.610 --> 00:52:18.310 align:middle line:90% divide that by total population. 00:52:18.310 --> 00:52:20.070 align:middle line:90% What's problematic with that? 00:52:20.070 --> 00:52:21.350 align:middle line:90% Alban, do you have? 00:52:21.350 --> 00:52:26.390 align:middle line:84% AUDIENCE: I think they add this population infected with COVID 00:52:26.390 --> 00:52:27.670 align:middle line:90% is probably the-- 00:52:27.670 --> 00:52:30.170 align:middle line:84% HAZHIR RAHMANDAD: Oh it might be the combination of the two. 00:52:30.170 --> 00:52:32.610 align:middle line:84% Sorry, I might have judged that too fast. 00:52:32.610 --> 00:52:34.390 align:middle line:90% So let me see-- 00:52:34.390 --> 00:52:37.030 align:middle line:84% AUDIENCE: It's on the right side of the [INAUDIBLE]. 00:52:37.030 --> 00:52:38.695 align:middle line:90% I put all the-- 00:52:38.695 --> 00:52:40.570 align:middle line:84% HAZHIR RAHMANDAD: Yes, let me-- you're right. 00:52:40.570 --> 00:52:42.300 align:middle line:90% So this is not unvaccinated. 00:52:42.300 --> 00:52:43.050 align:middle line:90% This is the total. 00:52:43.050 --> 00:52:43.830 align:middle line:90% Thank you. 00:52:43.830 --> 00:52:46.650 align:middle line:84% And so note that Russ did this right. 00:52:46.650 --> 00:52:51.530 align:middle line:84% We just didn't read his model before commenting on it. 00:52:51.530 --> 00:52:54.790 align:middle line:84% So the unvaccinated population with COVID 00:52:54.790 --> 00:52:56.670 align:middle line:84% plus vaccinated population with COVID 00:52:56.670 --> 00:52:59.270 align:middle line:84% are added up in this formulation. 00:52:59.270 --> 00:53:01.350 align:middle line:90% So that's good. 00:53:01.350 --> 00:53:04.110 align:middle line:84% That takes care of the first-order problem 00:53:04.110 --> 00:53:05.250 align:middle line:90% I highlighted. 00:53:05.250 --> 00:53:07.630 align:middle line:84% It does have one minor issue, and that 00:53:07.630 --> 00:53:10.950 align:middle line:84% is the question of whether the vaccinated people have 00:53:10.950 --> 00:53:15.930 align:middle line:84% the same infectivity, have the same risk of infecting others, 00:53:15.930 --> 00:53:17.550 align:middle line:90% as unvaccinated people. 00:53:17.550 --> 00:53:19.850 align:middle line:84% Russ, what was your thinking on that? 00:53:19.850 --> 00:53:25.170 align:middle line:84% AUDIENCE: I also calculated the infectivity as a weighted sum-- 00:53:25.170 --> 00:53:27.435 align:middle line:90% a weighted average between the-- 00:53:27.435 --> 00:53:29.310 align:middle line:84% HAZHIR RAHMANDAD: That's an interesting idea. 00:53:29.310 --> 00:53:32.370 align:middle line:84% So basically, for infectivity, you 00:53:32.370 --> 00:53:36.370 align:middle line:84% used some kind of a weighted average. 00:53:36.370 --> 00:53:39.550 align:middle line:84% So let's look at this formulation. 00:53:39.550 --> 00:53:43.030 align:middle line:84% Now, this is messy because Vensim diagram is not easy, 00:53:43.030 --> 00:53:44.830 align:middle line:84% and this long variable names don't help. 00:53:44.830 --> 00:53:48.010 align:middle line:84% But it's baseline infectivity multiplied 00:53:48.010 --> 00:53:52.290 align:middle line:84% by unvaccinated population divided by-- 00:53:52.290 --> 00:53:54.390 align:middle line:84% AUDIENCE: Proportion of unvaccinated-- 00:53:54.390 --> 00:53:55.530 align:middle line:90% HAZHIR RAHMANDAD: Uh-huh. 00:53:55.530 --> 00:53:58.090 align:middle line:84% AUDIENCE: And then for the proportion who is vaccinated, 00:53:58.090 --> 00:54:00.628 align:middle line:84% there is a vaccine effectiveness in reducing infectivity. 00:54:00.628 --> 00:54:01.670 align:middle line:90% HAZHIR RAHMANDAD: Got it. 00:54:01.670 --> 00:54:02.330 align:middle line:90% Got it. 00:54:02.330 --> 00:54:03.930 align:middle line:84% AUDIENCE: So we have the baseline [INAUDIBLE]? 00:54:03.930 --> 00:54:04.430 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:54:04.430 --> 00:54:04.530 align:middle line:90% AUDIENCE: --by that. 00:54:04.530 --> 00:54:04.990 align:middle line:90% HAZHIR RAHMANDAD: Yes. 00:54:04.990 --> 00:54:05.750 align:middle line:90% That makes sense. 00:54:05.750 --> 00:54:08.490 align:middle line:84% So this takes care of the problem 00:54:08.490 --> 00:54:09.870 align:middle line:90% we were just talking about. 00:54:09.870 --> 00:54:13.580 align:middle line:84% So this is a good formulation addressing the challenge 00:54:13.580 --> 00:54:15.140 align:middle line:90% we were talking about. 00:54:15.140 --> 00:54:19.120 align:middle line:84% That is, the total population that is infected works fine. 00:54:19.120 --> 00:54:22.420 align:middle line:90% The infectivity also works fine. 00:54:22.420 --> 00:54:27.480 align:middle line:84% And this is population weighted average. 00:54:27.480 --> 00:54:28.920 align:middle line:90% So this should be fine. 00:54:28.920 --> 00:54:35.780 align:middle line:90% Let me just-- yeah. 00:54:35.780 --> 00:54:38.246 align:middle line:90% This is good. 00:54:38.246 --> 00:54:41.660 align:middle line:84% So first, any questions on what is the problem 00:54:41.660 --> 00:54:44.260 align:middle line:84% we are trying to solve here, because we jumped through it 00:54:44.260 --> 00:54:45.600 align:middle line:90% a little bit too quickly? 00:54:45.600 --> 00:54:52.460 align:middle line:90% 00:54:52.460 --> 00:54:58.540 align:middle line:84% So basically, the basic problem was 00:54:58.540 --> 00:55:01.900 align:middle line:84% we have two types of infectious populations 00:55:01.900 --> 00:55:04.140 align:middle line:90% who could infect anybody. 00:55:04.140 --> 00:55:08.360 align:middle line:84% Those two types are those who are vaccinated and unvaccinated. 00:55:08.360 --> 00:55:10.280 align:middle line:84% Those who are vaccinated probably 00:55:10.280 --> 00:55:13.040 align:middle line:84% have lower risk of infecting others. 00:55:13.040 --> 00:55:16.520 align:middle line:84% So when we are calculating the total fraction of population 00:55:16.520 --> 00:55:19.600 align:middle line:84% that is infected, we want to calculate 00:55:19.600 --> 00:55:22.080 align:middle line:90% both of these as infected. 00:55:22.080 --> 00:55:24.440 align:middle line:84% But then the infectivity will change depending 00:55:24.440 --> 00:55:27.080 align:middle line:84% on there are more people who are vaccinated or less people who 00:55:27.080 --> 00:55:28.600 align:middle line:90% are vaccinated. 00:55:28.600 --> 00:55:34.640 align:middle line:84% This formulation creates a weighted infectivity that says, 00:55:34.640 --> 00:55:39.040 align:middle line:84% depending on which of these is a larger fraction, 00:55:39.040 --> 00:55:41.520 align:middle line:84% infectivity goes up or comes down. 00:55:41.520 --> 00:55:44.720 align:middle line:84% And this is doing it in an internally consistent way. 00:55:44.720 --> 00:55:47.680 align:middle line:84% So this would be a nice way to formulate it. 00:55:47.680 --> 00:55:54.660 align:middle line:84% A mathematically equivalent but a little bit simpler, 00:55:54.660 --> 00:55:56.920 align:middle line:84% even though potentially, conceptually, 00:55:56.920 --> 00:55:59.840 align:middle line:84% a little bit more murky way of doing it, 00:55:59.840 --> 00:56:03.040 align:middle line:84% would be to keep your baseline infectivity 00:56:03.040 --> 00:56:05.890 align:middle line:84% that you have as your infectivity. 00:56:05.890 --> 00:56:09.590 align:middle line:84% But then into the population infected with COVID, 00:56:09.590 --> 00:56:13.210 align:middle line:84% rather than calling it population infected with COVID, 00:56:13.210 --> 00:56:18.130 align:middle line:84% call it kind of population infected 00:56:18.130 --> 00:56:20.330 align:middle line:84% with COVID normalized for infectivity, 00:56:20.330 --> 00:56:22.130 align:middle line:90% or something like that. 00:56:22.130 --> 00:56:24.630 align:middle line:84% And then within that formulation, 00:56:24.630 --> 00:56:27.970 align:middle line:84% rather than using unvaccinated population 00:56:27.970 --> 00:56:31.050 align:middle line:84% plus vaccinated population, use unvaccinated population 00:56:31.050 --> 00:56:33.730 align:middle line:84% plus vaccinated population multiplied 00:56:33.730 --> 00:56:37.370 align:middle line:84% by that parameter that is the relative infectivity 00:56:37.370 --> 00:56:40.830 align:middle line:84% of vaccinated population to unvaccinated. 00:56:40.830 --> 00:56:42.650 align:middle line:84% So that parameter is always below 1. 00:56:42.650 --> 00:56:45.570 align:middle line:84% That kind of down weights this population. 00:56:45.570 --> 00:56:50.050 align:middle line:84% I'm 80% sure it's mathematically equivalent to what 00:56:50.050 --> 00:56:52.010 align:middle line:84% we are seeing here, but I haven't written down 00:56:52.010 --> 00:56:53.010 align:middle line:90% the equations. 00:56:53.010 --> 00:56:55.990 align:middle line:84% So both of those work, would be fine. 00:56:55.990 --> 00:57:00.690 align:middle line:84% Thanks, Russ, for doing it in a solid way. 00:57:00.690 --> 00:57:02.690 align:middle line:84% So now let's go to the perceived risk, 00:57:02.690 --> 00:57:05.445 align:middle line:84% because we said perceived risk, if it is-- oh, you 00:57:05.445 --> 00:57:06.570 align:middle line:90% have a question, Alexander. 00:57:06.570 --> 00:57:07.310 align:middle line:90% Go ahead. 00:57:07.310 --> 00:57:10.630 align:middle line:84% AUDIENCE: So is it an issue that there 00:57:10.630 --> 00:57:13.110 align:middle line:84% is no parameter controlling the effect of perceived 00:57:13.110 --> 00:57:15.150 align:middle line:90% risk on infection rate? 00:57:15.150 --> 00:57:16.030 align:middle line:90% [INAUDIBLE], yeah. 00:57:16.030 --> 00:57:18.270 align:middle line:84% HAZHIR RAHMANDAD: So it really depends on the meaning 00:57:18.270 --> 00:57:19.590 align:middle line:90% of perceived risk. 00:57:19.590 --> 00:57:25.590 align:middle line:84% So if the perceived risk is defined in a way 00:57:25.590 --> 00:57:28.510 align:middle line:84% that is well contained between 0 and 1, 00:57:28.510 --> 00:57:31.510 align:middle line:84% and then it would need parameters 00:57:31.510 --> 00:57:33.810 align:middle line:84% that measure its kind of strength, 00:57:33.810 --> 00:57:39.070 align:middle line:84% how fast it responds to cases, deaths, and so on. 00:57:39.070 --> 00:57:42.270 align:middle line:84% So let's take a look at this formulation here. 00:57:42.270 --> 00:57:44.950 align:middle line:84% We have indicated perceived risk. 00:57:44.950 --> 00:57:46.830 align:middle line:90% We have the COVID trend. 00:57:46.830 --> 00:57:50.950 align:middle line:84% And the COVID trend is coming from this COVID statistics, 00:57:50.950 --> 00:57:53.850 align:middle line:84% which depends on death versus infection rate, 00:57:53.850 --> 00:58:00.110 align:middle line:84% and the parameter that controls which of these has a bigger 00:58:00.110 --> 00:58:01.370 align:middle line:90% impact of sorts. 00:58:01.370 --> 00:58:05.000 align:middle line:84% So this sensitivity to death is-- 00:58:05.000 --> 00:58:08.240 align:middle line:90% so this formulation is OK. 00:58:08.240 --> 00:58:11.020 align:middle line:84% It will take care of what you are trying to do. 00:58:11.020 --> 00:58:14.120 align:middle line:84% But then you have to have a large number for sensitivity 00:58:14.120 --> 00:58:17.800 align:middle line:84% to death, probably, to make it comparable with the infection 00:58:17.800 --> 00:58:18.680 align:middle line:90% rate. 00:58:18.680 --> 00:58:21.120 align:middle line:84% So you're going with 10 times here. 00:58:21.120 --> 00:58:21.900 align:middle line:90% That's fine. 00:58:21.900 --> 00:58:27.860 align:middle line:84% And to be honest, I'm also fine with doing no impact of cases, 00:58:27.860 --> 00:58:30.560 align:middle line:90% just doing an impact of deaths. 00:58:30.560 --> 00:58:33.920 align:middle line:84% And by the way, we don't want unit errors. 00:58:33.920 --> 00:58:37.240 align:middle line:84% Then this COVID statistics things 00:58:37.240 --> 00:58:45.620 align:middle line:84% goes into basically a delay, a trend function of sorts. 00:58:45.620 --> 00:58:48.600 align:middle line:90% 00:58:48.600 --> 00:58:50.120 align:middle line:90% What's happening? 00:58:50.120 --> 00:58:52.240 align:middle line:90% Ah, yes. 00:58:52.240 --> 00:59:02.820 align:middle line:84% So this is a fixed delay of COVID statistics with a time-- 00:59:02.820 --> 00:59:05.140 align:middle line:90% with a delay length of 1. 00:59:05.140 --> 00:59:10.060 align:middle line:84% So first of all, what is this formulation trying to do? 00:59:10.060 --> 00:59:12.760 align:middle line:84% So Russ, do you want to tell what it is trying to do? 00:59:12.760 --> 00:59:17.525 align:middle line:90% 00:59:17.525 --> 00:59:18.900 align:middle line:84% AUDIENCE: So I remember every day 00:59:18.900 --> 00:59:21.900 align:middle line:84% we had the COVID statistics during the COVID time, 00:59:21.900 --> 00:59:23.873 align:middle line:84% and I was trying to capture the slope. 00:59:23.873 --> 00:59:25.040 align:middle line:90% HAZHIR RAHMANDAD: Very good. 00:59:25.040 --> 00:59:27.740 align:middle line:84% So basically, to capture the slope, 00:59:27.740 --> 00:59:31.720 align:middle line:84% Russ is creating a one-day delayed version of that thing, 00:59:31.720 --> 00:59:34.820 align:middle line:84% and then compares it with whatever the thing is, and then 00:59:34.820 --> 00:59:36.480 align:middle line:90% creates the slope using that. 00:59:36.480 --> 00:59:39.860 align:middle line:84% So it's basically one way of doing the trend function. 00:59:39.860 --> 00:59:42.200 align:middle line:90% Now, I don't like fixed delays. 00:59:42.200 --> 00:59:45.380 align:middle line:84% So by and large, in this course, don't use fixed delays. 00:59:45.380 --> 00:59:47.340 align:middle line:90% There are two reasons for it. 00:59:47.340 --> 00:59:50.340 align:middle line:84% One is that under each fixed delay, 00:59:50.340 --> 00:59:54.660 align:middle line:84% Vensim creates a large number of stock variables-- 00:59:54.660 --> 00:59:57.460 align:middle line:84% state variables-- to capture the fixed delay. 00:59:57.460 --> 00:59:59.800 align:middle line:84% The number it creates is the time 00:59:59.800 --> 01:00:03.100 align:middle line:84% of the delay divided by the time step for simulation. 01:00:03.100 --> 01:00:07.380 align:middle line:84% So if your time step for simulation is 1/100ths of a day, 01:00:07.380 --> 01:00:10.865 align:middle line:84% then you have 100 stocks hidden behind this fixed delay, 01:00:10.865 --> 01:00:13.240 align:middle line:84% which you have no idea of how things are happening inside 01:00:13.240 --> 01:00:13.740 align:middle line:90% them. 01:00:13.740 --> 01:00:15.240 align:middle line:90% So that's number one. 01:00:15.240 --> 01:00:18.240 align:middle line:84% Number two is that partly because of this reason, 01:00:18.240 --> 01:00:21.060 align:middle line:84% fixed delays do behaviors that are weird, 01:00:21.060 --> 01:00:23.920 align:middle line:84% that are hard to explain because you can't trace their-- 01:00:23.920 --> 01:00:27.080 align:middle line:90% they're very sharp behaviors. 01:00:27.080 --> 01:00:30.860 align:middle line:84% So even though mathematically, sometimes it is a useful thing, 01:00:30.860 --> 01:00:34.160 align:middle line:84% you may want to use it, it's not usually the best thing. 01:00:34.160 --> 01:00:38.160 align:middle line:84% And that noisiness is also-- in a noisiness a stochastic model, 01:00:38.160 --> 01:00:39.580 align:middle line:90% creates lots of problems. 01:00:39.580 --> 01:00:42.860 align:middle line:84% So that's kind of you don't want it for that purpose. 01:00:42.860 --> 01:00:45.220 align:middle line:84% But conceptually, what Russ is doing is fine. 01:00:45.220 --> 01:00:47.040 align:middle line:84% He's just trying to take a derivative 01:00:47.040 --> 01:00:50.400 align:middle line:84% of some variable, which is basically these COVID 01:00:50.400 --> 01:00:52.960 align:middle line:90% statistics. 01:00:52.960 --> 01:00:54.820 align:middle line:84% And this creates the COVID trend. 01:00:54.820 --> 01:00:57.210 align:middle line:84% In fact, you could use the built-in trend 01:00:57.210 --> 01:00:59.930 align:middle line:84% function in Vensim to get perhaps to the same thing. 01:00:59.930 --> 01:01:01.930 align:middle line:84% It's just the difference between the two divided 01:01:01.930 --> 01:01:06.690 align:middle line:84% by delayed COVID statistics plus this number 01:01:06.690 --> 01:01:09.250 align:middle line:90% to avoid division by 0. 01:01:09.250 --> 01:01:14.610 align:middle line:84% Now, all of that is fine, but adding a number to the equation 01:01:14.610 --> 01:01:21.010 align:middle line:84% is not really the best way to avoid division by 0. 01:01:21.010 --> 01:01:22.610 align:middle line:84% Even if you want to add it, you want 01:01:22.610 --> 01:01:25.130 align:middle line:84% to have a separate parameter named for it so that you 01:01:25.130 --> 01:01:27.150 align:middle line:90% don't lose unit consistency. 01:01:27.150 --> 01:01:31.330 align:middle line:84% This will be a source of unit problems for you. 01:01:31.330 --> 01:01:37.950 align:middle line:84% The better way might be using a ZIDZ or XIDZ function, 01:01:37.950 --> 01:01:39.410 align:middle line:90% which is just a division. 01:01:39.410 --> 01:01:43.050 align:middle line:84% But if the denominator is 0, you can 01:01:43.050 --> 01:01:47.950 align:middle line:84% specify what is the output of that division in XIDZ or ZIDZ, 01:01:47.950 --> 01:01:51.130 align:middle line:90% which is the output is 0. 01:01:51.130 --> 01:01:55.150 align:middle line:90% And I think that's fine. 01:01:55.150 --> 01:01:57.910 align:middle line:84% Now, conceptually, this formulation 01:01:57.910 --> 01:02:02.190 align:middle line:84% is taking the derivative of deaths or cases, infection rate 01:02:02.190 --> 01:02:03.670 align:middle line:90% or death rate. 01:02:03.670 --> 01:02:06.990 align:middle line:84% So why do we care about the derivative, Russ, rather than 01:02:06.990 --> 01:02:09.850 align:middle line:84% the current value of death rate or infection rate? 01:02:09.850 --> 01:02:11.530 align:middle line:90% What is that idea? 01:02:11.530 --> 01:02:13.490 align:middle line:84% What's the driver of that idea for you? 01:02:13.490 --> 01:02:16.830 align:middle line:90% 01:02:16.830 --> 01:02:21.190 align:middle line:84% AUDIENCE: I just thought the risk response to risk 01:02:21.190 --> 01:02:24.230 align:middle line:84% is usually comes from the philosophy 01:02:24.230 --> 01:02:28.910 align:middle line:84% that people feel about whether it is getting better or worse 01:02:28.910 --> 01:02:31.510 align:middle line:90% compared to yesterday, I guess. 01:02:31.510 --> 01:02:32.710 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:02:32.710 --> 01:02:37.410 align:middle line:84% So this is actually an important kind of question. 01:02:37.410 --> 01:02:39.810 align:middle line:84% What is driving people's risk perception? 01:02:39.810 --> 01:02:44.030 align:middle line:84% Is it the change in risk, the way they see it? 01:02:44.030 --> 01:02:46.990 align:middle line:84% Or is it the current level of risk? 01:02:46.990 --> 01:02:51.030 align:middle line:84% So if the number of cases are coming down, 01:02:51.030 --> 01:02:54.640 align:middle line:84% does it mean I would feel completely safe now 01:02:54.640 --> 01:02:57.800 align:middle line:84% because it is a negative number, and therefore, I 01:02:57.800 --> 01:02:59.840 align:middle line:84% should feel even better than when 01:02:59.840 --> 01:03:03.660 align:middle line:84% there was no COVID, because when there is no COVID, 01:03:03.660 --> 01:03:06.120 align:middle line:90% the trend is 0. 01:03:06.120 --> 01:03:09.280 align:middle line:84% So now I feel I should go out and party every day 01:03:09.280 --> 01:03:13.410 align:middle line:84% because the number of cases per day are coming down from 3,000 01:03:13.410 --> 01:03:17.400 align:middle line:90% to 2,500 deaths per day. 01:03:17.400 --> 01:03:21.760 align:middle line:84% Or I should feel less worried than yesterday, 01:03:21.760 --> 01:03:25.720 align:middle line:90% but not completely unworried. 01:03:25.720 --> 01:03:26.940 align:middle line:90% So that's the question. 01:03:26.940 --> 01:03:29.260 align:middle line:84% And I think the answer is largely clear in this case. 01:03:29.260 --> 01:03:32.320 align:middle line:84% That is, it is not the trend of death and case 01:03:32.320 --> 01:03:36.960 align:middle line:84% that determines the absolute value of risk perception. 01:03:36.960 --> 01:03:39.880 align:middle line:84% Rather, it is the absolute value of risk 01:03:39.880 --> 01:03:43.460 align:middle line:84% that determines the absolute value of the perceived risk. 01:03:43.460 --> 01:03:48.800 align:middle line:84% So you actually don't even need all of these trend stuff here. 01:03:48.800 --> 01:03:53.400 align:middle line:84% And then the indicated perceived risk is doing-- 01:03:53.400 --> 01:03:59.340 align:middle line:90% 01:03:59.340 --> 01:04:02.780 align:middle line:84% AUDIENCE: I'm using a sigmoid function, like a logic function, 01:04:02.780 --> 01:04:04.500 align:middle line:90% that is centered on 0. 01:04:04.500 --> 01:04:06.220 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:04:06.220 --> 01:04:08.820 align:middle line:84% AUDIENCE: And then-- because the trend 01:04:08.820 --> 01:04:11.820 align:middle line:84% is something that is just any real number, such that it 01:04:11.820 --> 01:04:14.180 align:middle line:90% might fit into some interval. 01:04:14.180 --> 01:04:15.340 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:04:15.340 --> 01:04:17.460 align:middle line:84% AUDIENCE: And then center in into 0. 01:04:17.460 --> 01:04:20.100 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:04:20.100 --> 01:04:26.500 align:middle line:84% AUDIENCE: So when there is 0 COVID trend, then-- 01:04:26.500 --> 01:04:29.860 align:middle line:84% HAZHIR RAHMANDAD: The function becomes minus 0.5. 01:04:29.860 --> 01:04:31.385 align:middle line:84% AUDIENCE: The whole thing becomes 0. 01:04:31.385 --> 01:04:32.260 align:middle line:90% HAZHIR RAHMANDAD: Oh. 01:04:32.260 --> 01:04:32.700 align:middle line:90% Does it? 01:04:32.700 --> 01:04:33.080 align:middle line:90% OK. 01:04:33.080 --> 01:04:33.580 align:middle line:90% Sorry. 01:04:33.580 --> 01:04:36.475 align:middle line:84% AUDIENCE: Because it is centered at 0 by subtracting 0.5. 01:04:36.475 --> 01:04:38.100 align:middle line:84% HAZHIR RAHMANDAD: Oh, Yeah, yeah, yeah. 01:04:38.100 --> 01:04:38.640 align:middle line:90% You're right. 01:04:38.640 --> 01:04:39.182 align:middle line:90% You're right. 01:04:39.182 --> 01:04:40.680 align:middle line:90% So e to the power of thing. 01:04:40.680 --> 01:04:41.455 align:middle line:90% Yeah. 01:04:41.455 --> 01:04:42.080 align:middle line:90% AUDIENCE: Yeah. 01:04:42.080 --> 01:04:44.780 align:middle line:84% So when trend is increasing, then it's 01:04:44.780 --> 01:04:46.280 align:middle line:84% going to be some positive number. 01:04:46.280 --> 01:04:49.310 align:middle line:84% When it's decreasing, it's negative number. 01:04:49.310 --> 01:04:53.630 align:middle line:84% HAZHIR RAHMANDAD: So let's say trend is negative infinity. 01:04:53.630 --> 01:04:57.110 align:middle line:84% Then this function becomes minus 5-- 01:04:57.110 --> 01:04:57.970 align:middle line:90% 0.5. 01:04:57.970 --> 01:04:59.150 align:middle line:90% Correct? 01:04:59.150 --> 01:04:59.950 align:middle line:90% AUDIENCE: Yeah. 01:04:59.950 --> 01:05:02.990 align:middle line:84% HAZHIR RAHMANDAD: Which means people will be interacting 01:05:02.990 --> 01:05:06.765 align:middle line:90% more than they normally do. 01:05:06.765 --> 01:05:07.390 align:middle line:90% AUDIENCE: Yeah. 01:05:07.390 --> 01:05:08.807 align:middle line:84% HAZHIR RAHMANDAD: So there is kind 01:05:08.807 --> 01:05:10.790 align:middle line:84% of the possibility in this function 01:05:10.790 --> 01:05:12.810 align:middle line:90% that people actually interact. 01:05:12.810 --> 01:05:15.950 align:middle line:84% Remember, in the next step, infection rate 01:05:15.950 --> 01:05:20.270 align:middle line:90% is 1 minus this thing. 01:05:20.270 --> 01:05:31.070 align:middle line:84% So if you make that 1.5, you're increasing the infection rate-- 01:05:31.070 --> 01:05:31.990 align:middle line:90% AUDIENCE: Yeah. 01:05:31.990 --> 01:05:35.130 align:middle line:84% HAZHIR RAHMANDAD: --when the trend is a very negative number. 01:05:35.130 --> 01:05:38.390 align:middle line:90% So this is not going to work. 01:05:38.390 --> 01:05:42.170 align:middle line:84% First of all, your next function, 01:05:42.170 --> 01:05:48.570 align:middle line:84% which is when this trend thing goes into the infection rate, 01:05:48.570 --> 01:05:50.630 align:middle line:90% this has 1 minus perceived risk. 01:05:50.630 --> 01:05:53.410 align:middle line:90% 01:05:53.410 --> 01:05:55.370 align:middle line:84% So this 1 minus perceived risk, I 01:05:55.370 --> 01:05:59.770 align:middle line:84% don't want it to go ever below 0 or above 1, 01:05:59.770 --> 01:06:03.010 align:middle line:84% because otherwise I lose control of how I'm 01:06:03.010 --> 01:06:04.550 align:middle line:90% thinking about this function. 01:06:04.550 --> 01:06:05.990 align:middle line:84% It becomes a very messy function. 01:06:05.990 --> 01:06:10.830 align:middle line:84% So this is my constraint for this function. 01:06:10.830 --> 01:06:15.330 align:middle line:84% And right now, I can see that it can actually go to above 1. 01:06:15.330 --> 01:06:20.650 align:middle line:90% Now, could it go below 0? 01:06:20.650 --> 01:06:26.690 align:middle line:84% For it to go below 0, you need the other part to go above 1. 01:06:26.690 --> 01:06:30.750 align:middle line:90% Could this ratio go above 1? 01:06:30.750 --> 01:06:32.110 align:middle line:90% No, it can't go above 1. 01:06:32.110 --> 01:06:35.710 align:middle line:84% So that ratio will always be below 1. 01:06:35.710 --> 01:06:40.050 align:middle line:84% So at least it wouldn't have the very extreme lack 01:06:40.050 --> 01:06:45.820 align:middle line:84% of robustness that pushes your infection rate 01:06:45.820 --> 01:06:48.620 align:middle line:90% to become negative, because-- 01:06:48.620 --> 01:06:49.560 align:middle line:90% yes, Russ? 01:06:49.560 --> 01:06:53.900 align:middle line:84% AUDIENCE: I was trying to capture the perceived risk, 01:06:53.900 --> 01:06:58.980 align:middle line:84% and then make it adjust the infectivity infection 01:06:58.980 --> 01:07:06.820 align:middle line:84% rate from 50% to 150% compared to the regular level. 01:07:06.820 --> 01:07:08.748 align:middle line:90% I guess it is restricted. 01:07:08.748 --> 01:07:11.040 align:middle line:84% HAZHIR RAHMANDAD: Well, one thing is being restrictive. 01:07:11.040 --> 01:07:16.520 align:middle line:84% The other is that by making it 150% compared to the baseline, 01:07:16.520 --> 01:07:19.260 align:middle line:84% you are basically incorporating a situation 01:07:19.260 --> 01:07:22.140 align:middle line:84% that, as a result of the dynamics in the model, 01:07:22.140 --> 01:07:26.260 align:middle line:84% people's infection rate and people's interaction levels that 01:07:26.260 --> 01:07:31.020 align:middle line:84% create those infection rates go above and beyond what they would 01:07:31.020 --> 01:07:33.242 align:middle line:90% be absent any of the disease. 01:07:33.242 --> 01:07:34.700 align:middle line:84% That is, you are saying people will 01:07:34.700 --> 01:07:38.380 align:middle line:84% start to interact even more than when there is no disease. 01:07:38.380 --> 01:07:40.940 align:middle line:84% That's just not physically right. 01:07:40.940 --> 01:07:44.920 align:middle line:90% That's the problem. 01:07:44.920 --> 01:07:46.600 align:middle line:84% AUDIENCE: Can I add another concern? 01:07:46.600 --> 01:07:51.320 align:middle line:84% The fact that this cannot actually shut down infection, 01:07:51.320 --> 01:07:54.483 align:middle line:84% even in a very extreme case, I think that is concerning, too. 01:07:54.483 --> 01:07:55.400 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:07:55.400 --> 01:07:59.880 align:middle line:84% So you are saying that if the trend-- and the trend 01:07:59.880 --> 01:08:00.660 align:middle line:90% is a problem. 01:08:00.660 --> 01:08:01.940 align:middle line:90% So let's put that aside. 01:08:01.940 --> 01:08:03.980 align:middle line:84% But let's say this goes to infinity, 01:08:03.980 --> 01:08:06.640 align:middle line:90% the trend is very large number. 01:08:06.640 --> 01:08:12.640 align:middle line:90% So this ratio becomes minus 0.5. 01:08:12.640 --> 01:08:15.660 align:middle line:84% And therefore-- sorry, not minus 0.5. 01:08:15.660 --> 01:08:16.160 align:middle line:90% Sorry. 01:08:16.160 --> 01:08:20.760 align:middle line:84% It becomes a 0.5 because it is 1 minus 0.5. 01:08:20.760 --> 01:08:26.160 align:middle line:84% So then it will never go below 50% of the baseline. 01:08:26.160 --> 01:08:31.479 align:middle line:84% So you are imposing another kind of a lower bound 01:08:31.479 --> 01:08:35.399 align:middle line:84% on the interaction in the population that 01:08:35.399 --> 01:08:37.540 align:middle line:90% is baked into your formulation. 01:08:37.540 --> 01:08:39.040 align:middle line:84% So it is OK to have a lower bound. 01:08:39.040 --> 01:08:43.050 align:middle line:84% You may say the population interaction will never 01:08:43.050 --> 01:08:48.149 align:middle line:84% go under 10% of its baseline, or whatever you think is feasible. 01:08:48.149 --> 01:08:51.310 align:middle line:84% But if it is baked into the structure of your formulation, 01:08:51.310 --> 01:08:55.390 align:middle line:84% you will never recover understand that failure mode. 01:08:55.390 --> 01:08:59.149 align:middle line:84% So that's another reason why this formulation is problematic. 01:08:59.149 --> 01:09:04.130 align:middle line:84% So I think that was good discussion on the formulation. 01:09:04.130 --> 01:09:07.090 align:middle line:84% Let's take a look at the vaccination process. 01:09:07.090 --> 01:09:14.810 align:middle line:84% So we are getting some fraction of population getting vaccinated 01:09:14.810 --> 01:09:17.810 align:middle line:84% here, or some number of population getting vaccinated 01:09:17.810 --> 01:09:18.450 align:middle line:90% here. 01:09:18.450 --> 01:09:21.890 align:middle line:84% And the formulation is the maximum vaccination capacity 01:09:21.890 --> 01:09:26.529 align:middle line:84% per day, minimum of maximum vaccination per day, multiplied 01:09:26.529 --> 01:09:28.330 align:middle line:84% by fraction of population willing 01:09:28.330 --> 01:09:32.170 align:middle line:84% multiplied by unvaccinated population susceptible to COVID. 01:09:32.170 --> 01:09:35.729 align:middle line:84% So I think the idea that Russ is trying to capture here 01:09:35.729 --> 01:09:40.850 align:middle line:84% is there is a maximum capacity-- so we put the maximum capacity-- 01:09:40.850 --> 01:09:42.390 align:middle line:84% and then a fraction of population 01:09:42.390 --> 01:09:44.550 align:middle line:90% is willing to vaccinate. 01:09:44.550 --> 01:09:46.510 align:middle line:90% Out of that fraction-- 01:09:46.510 --> 01:09:51.029 align:middle line:84% so we multiply that fraction by unvaccinated population that 01:09:51.029 --> 01:09:54.510 align:middle line:90% remains susceptible to COVID. 01:09:54.510 --> 01:09:58.885 align:middle line:90% So what's problematic here? 01:09:58.885 --> 01:09:59.510 align:middle line:90% AUDIENCE: Unit? 01:09:59.510 --> 01:10:01.655 align:middle line:90% 01:10:01.655 --> 01:10:03.030 align:middle line:84% HAZHIR RAHMANDAD: Actually, units 01:10:03.030 --> 01:10:06.990 align:middle line:84% should be fine if you make the fraction willing to get 01:10:06.990 --> 01:10:08.570 align:middle line:90% vaccinated 1 over year. 01:10:08.570 --> 01:10:11.550 align:middle line:84% Otherwise, you're right, the units will be a problem. 01:10:11.550 --> 01:10:16.390 align:middle line:84% So I think the unit part is actually informative, 01:10:16.390 --> 01:10:18.470 align:middle line:84% because if you think about it, then 01:10:18.470 --> 01:10:21.330 align:middle line:84% you see that the variable naming is problematic. 01:10:21.330 --> 01:10:23.890 align:middle line:84% If you're calling it fraction willing to get vaccinated, 01:10:23.890 --> 01:10:26.470 align:middle line:84% that should be a dimensionless concept. 01:10:26.470 --> 01:10:28.230 align:middle line:84% But here, for the unit consistency, 01:10:28.230 --> 01:10:31.290 align:middle line:84% it has to be 1 over unit of time. 01:10:31.290 --> 01:10:33.450 align:middle line:84% My guess is that it is dimensionless. 01:10:33.450 --> 01:10:36.200 align:middle line:90% We'll see. 01:10:36.200 --> 01:10:39.480 align:middle line:84% Russ, which one do you want to do? 01:10:39.480 --> 01:10:40.480 align:middle line:90% Yes, it is. 01:10:40.480 --> 01:10:43.640 align:middle line:90% It is a dimensionless one. 01:10:43.640 --> 01:10:49.800 align:middle line:84% So basically, it is missing the whole time for vaccination. 01:10:49.800 --> 01:10:52.060 align:middle line:84% And therefore, this is a good unit problem. 01:10:52.060 --> 01:10:55.320 align:middle line:84% That is good in the sense that if you had done the unit 01:10:55.320 --> 01:10:57.120 align:middle line:84% analysis, you would have said, oh, I'm 01:10:57.120 --> 01:10:59.380 align:middle line:84% missing actually a conceptual variable here 01:10:59.380 --> 01:11:01.360 align:middle line:90% about time to get vaccinated. 01:11:01.360 --> 01:11:05.360 align:middle line:90% What else is problematic? 01:11:05.360 --> 01:11:07.040 align:middle line:90% Alexander? 01:11:07.040 --> 01:11:09.080 align:middle line:84% AUDIENCE: If there were no outflow 01:11:09.080 --> 01:11:12.480 align:middle line:84% from the unvaccinated population susceptible to COVID, 01:11:12.480 --> 01:11:15.360 align:middle line:84% like let's say that was the only outflow and the only flow 01:11:15.360 --> 01:11:17.740 align:middle line:84% from it, then everyone would eventually get vaccinated, 01:11:17.740 --> 01:11:21.442 align:middle line:84% when we were saying that it's only a fraction that would. 01:11:21.442 --> 01:11:22.400 align:middle line:90% HAZHIR RAHMANDAD: Good. 01:11:22.400 --> 01:11:25.420 align:middle line:84% So are you folks following this critique? 01:11:25.420 --> 01:11:28.520 align:middle line:90% So Alexander's point was that-- 01:11:28.520 --> 01:11:31.920 align:middle line:84% take an extreme condition case where the unvaccinated 01:11:31.920 --> 01:11:36.760 align:middle line:84% population susceptible to COVID was our only stock-- 01:11:36.760 --> 01:11:39.900 align:middle line:84% we didn't care about their infection, and so on-- 01:11:39.900 --> 01:11:42.940 align:middle line:84% and we just wanted to track vaccination. 01:11:42.940 --> 01:11:45.765 align:middle line:84% In that case, mentally simulate-- 01:11:45.765 --> 01:11:47.140 align:middle line:84% and let's say you don't care also 01:11:47.140 --> 01:11:49.640 align:middle line:84% about the infections on the top just to keep things simple. 01:11:49.640 --> 01:11:52.140 align:middle line:84% You're just looking at people moving to the left-hand side-- 01:11:52.140 --> 01:11:53.660 align:middle line:90% two stocks. 01:11:53.660 --> 01:11:57.420 align:middle line:84% In that extreme case, what you want-- 01:11:57.420 --> 01:12:00.180 align:middle line:84% you're trying to set it up so that 80% of people 01:12:00.180 --> 01:12:02.340 align:middle line:90% get vaccinated and no more. 01:12:02.340 --> 01:12:07.013 align:middle line:84% But would 80% get vaccinated here? 01:12:07.013 --> 01:12:08.180 align:middle line:90% AUDIENCE: All of them would. 01:12:08.180 --> 01:12:11.140 align:middle line:84% HAZHIR RAHMANDAD: All of them would because the flow variable 01:12:11.140 --> 01:12:13.020 align:middle line:90% will never shut off. 01:12:13.020 --> 01:12:16.540 align:middle line:84% The flow variable of vaccination rate 01:12:16.540 --> 01:12:18.500 align:middle line:84% will always remain positive as long 01:12:18.500 --> 01:12:21.340 align:middle line:84% as you have unvaccinated population. 01:12:21.340 --> 01:12:23.800 align:middle line:84% And therefore, it will vaccinate everybody. 01:12:23.800 --> 01:12:26.660 align:middle line:90% 01:12:26.660 --> 01:12:30.900 align:middle line:84% So how would you tackle that problem? 01:12:30.900 --> 01:12:32.920 align:middle line:90% Jason? 01:12:32.920 --> 01:12:35.640 align:middle line:84% AUDIENCE: This might not be correct. 01:12:35.640 --> 01:12:39.880 align:middle line:84% You could have some sort of gap-closing logic where you 01:12:39.880 --> 01:12:42.660 align:middle line:84% calculate indicated vaccinated population, 01:12:42.660 --> 01:12:46.480 align:middle line:84% and then as the actual vaccinated population approaches 01:12:46.480 --> 01:12:51.680 align:middle line:84% that level, the flow goes to 0, because now 01:12:51.680 --> 01:12:52.680 align:middle line:90% we're at the indicated-- 01:12:52.680 --> 01:12:56.040 align:middle line:84% HAZHIR RAHMANDAD: So how do you calculate that indicated? 01:12:56.040 --> 01:12:56.560 align:middle line:90% Yes. 01:12:56.560 --> 01:12:58.660 align:middle line:84% AUDIENCE: The way I did it was similar to Russ. 01:12:58.660 --> 01:13:01.720 align:middle line:84% I had a fraction willing to get the vaccine, 01:13:01.720 --> 01:13:07.440 align:middle line:84% and an indicated level, the indicated vaccinated population 01:13:07.440 --> 01:13:15.200 align:middle line:84% here is the sum of the unvaccinated susceptibles 01:13:15.200 --> 01:13:22.160 align:middle line:84% and the vaccinated population times that fraction. 01:13:22.160 --> 01:13:23.220 align:middle line:90% So yeah. 01:13:23.220 --> 01:13:27.285 align:middle line:90% 01:13:27.285 --> 01:13:28.160 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:13:28.160 --> 01:13:31.970 align:middle line:84% I think to follow what you did, we need to open your model. 01:13:31.970 --> 01:13:36.890 align:middle line:84% I couldn't mentally follow all of those steps. 01:13:36.890 --> 01:13:38.070 align:middle line:90% AUDIENCE: So mine-- 01:13:38.070 --> 01:13:41.395 align:middle line:84% I did do this robustness test and it seemed to work. 01:13:41.395 --> 01:13:42.270 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:13:42.270 --> 01:13:44.350 align:middle line:90% Well let's take a look at it. 01:13:44.350 --> 01:13:49.650 align:middle line:84% So basically, here is Jason's third model-- 01:13:49.650 --> 01:13:51.070 align:middle line:90% AUDIENCE: Vaccination pop. 01:13:51.070 --> 01:13:53.290 align:middle line:84% You see it right there in the center of the screen. 01:13:53.290 --> 01:13:56.070 align:middle line:84% HAZHIR RAHMANDAD: So this is the-- 01:13:56.070 --> 01:13:57.770 align:middle line:90% AUDIENCE: To the left. 01:13:57.770 --> 01:14:00.170 align:middle line:84% HAZHIR RAHMANDAD: --susceptible vaccinated is left, yes. 01:14:00.170 --> 01:14:02.770 align:middle line:90% 01:14:02.770 --> 01:14:06.190 align:middle line:84% And what we are looking at is vaccination rate. 01:14:06.190 --> 01:14:09.050 align:middle line:90% 01:14:09.050 --> 01:14:12.630 align:middle line:90% And vaccination rate is here. 01:14:12.630 --> 01:14:13.450 align:middle line:90% AUDIENCE: Yep. 01:14:13.450 --> 01:14:15.075 align:middle line:84% HAZHIR RAHMANDAD: So you have capacity. 01:14:15.075 --> 01:14:16.090 align:middle line:90% That's fine. 01:14:16.090 --> 01:14:19.770 align:middle line:84% And then you have the desired vaccination. 01:14:19.770 --> 01:14:23.570 align:middle line:84% Desired vaccination is fraction of population 01:14:23.570 --> 01:14:28.030 align:middle line:84% interested in vaccine into the indicated vaccine population. 01:14:28.030 --> 01:14:30.750 align:middle line:84% What is indicated vax population? 01:14:30.750 --> 01:14:35.390 align:middle line:84% AUDIENCE: That is the Size Of the population who 01:14:35.390 --> 01:14:37.310 align:middle line:90% desires vaccine? 01:14:37.310 --> 01:14:39.760 align:middle line:84% It includes the people who have vaccine. 01:14:39.760 --> 01:14:42.010 align:middle line:84% HAZHIR RAHMANDAD: OK, let me see how it is formulated. 01:14:42.010 --> 01:14:47.430 align:middle line:84% So it's susceptible vaccinated plus susceptible unvaccinated 01:14:47.430 --> 01:14:49.410 align:middle line:84% multiplied by fraction of population 01:14:49.410 --> 01:14:51.630 align:middle line:90% interested in vaccine. 01:14:51.630 --> 01:14:52.430 align:middle line:90% AUDIENCE: Yep. 01:14:52.430 --> 01:14:55.290 align:middle line:84% HAZHIR RAHMANDAD: So this is not going to work. 01:14:55.290 --> 01:14:57.670 align:middle line:84% So the reason this is not going to work 01:14:57.670 --> 01:15:06.750 align:middle line:84% is that this is not accounting for the total population. 01:15:06.750 --> 01:15:09.070 align:middle line:84% It is kind of you have all these other stocks that 01:15:09.070 --> 01:15:12.870 align:middle line:84% are missing from the calculation of what fraction-- how 01:15:12.870 --> 01:15:16.070 align:middle line:84% many people remain susceptible who 01:15:16.070 --> 01:15:19.770 align:middle line:84% are not vaccinated but willing to vaccinate. 01:15:19.770 --> 01:15:21.010 align:middle line:90% That's the number you need. 01:15:21.010 --> 01:15:24.750 align:middle line:90% 01:15:24.750 --> 01:15:27.240 align:middle line:84% AUDIENCE: And we actually have some unvaccinated infected, 01:15:27.240 --> 01:15:28.760 align:middle line:90% too, which should be-- 01:15:28.760 --> 01:15:30.260 align:middle line:84% HAZHIR RAHMANDAD: You have recovered 01:15:30.260 --> 01:15:34.840 align:middle line:84% people who are vaccinated and unvaccinated. 01:15:34.840 --> 01:15:35.880 align:middle line:90% AUDIENCE: That's true. 01:15:35.880 --> 01:15:37.463 align:middle line:84% HAZHIR RAHMANDAD: It is missing from-- 01:15:37.463 --> 01:15:40.280 align:middle line:90% yeah, you we could-- 01:15:40.280 --> 01:15:43.320 align:middle line:90% so OK. 01:15:43.320 --> 01:15:44.880 align:middle line:84% Let's look at one of the other models 01:15:44.880 --> 01:15:48.180 align:middle line:84% just so that we have one that is working on this front, 01:15:48.180 --> 01:15:51.040 align:middle line:84% so that-- because this is a little bit more complex, just 01:15:51.040 --> 01:15:52.860 align:middle line:84% talking on the air wouldn't work. 01:15:52.860 --> 01:15:58.880 align:middle line:90% So let's look at Hesam's model. 01:15:58.880 --> 01:16:00.360 align:middle line:90% Do you have that? 01:16:00.360 --> 01:16:01.840 align:middle line:84% AUDIENCE: Yeah, I have something. 01:16:01.840 --> 01:16:03.300 align:middle line:84% So I don't have the pressure there, 01:16:03.300 --> 01:16:05.400 align:middle line:84% but I have the indicated vax population 01:16:05.400 --> 01:16:07.620 align:middle line:84% is the fraction times the total population. 01:16:07.620 --> 01:16:09.370 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so the other thing 01:16:09.370 --> 01:16:11.560 align:middle line:84% was that pressure thing was a little bit harder 01:16:11.560 --> 01:16:15.740 align:middle line:84% to follow for me, so we needed to unpack that one. 01:16:15.740 --> 01:16:18.162 align:middle line:84% AUDIENCE: I have another one, I have a subscripted model. 01:16:18.162 --> 01:16:19.120 align:middle line:90% HAZHIR RAHMANDAD: I see 01:16:19.120 --> 01:16:21.867 align:middle line:84% AUDIENCE: It has an assumption, which is true. 01:16:21.867 --> 01:16:23.700 align:middle line:84% HAZHIR RAHMANDAD: So this is not vaccinated. 01:16:23.700 --> 01:16:25.158 align:middle line:84% AUDIENCE: It does have vaccination, 01:16:25.158 --> 01:16:27.520 align:middle line:84% but this one's assuming perfect immunity for vaccinated. 01:16:27.520 --> 01:16:29.937 align:middle line:84% So I have another [INAUDIBLE] which is a subsequent model. 01:16:29.937 --> 01:16:30.978 align:middle line:90% HAZHIR RAHMANDAD: Got it. 01:16:30.978 --> 01:16:32.980 align:middle line:84% AUDIENCE: It has a [? C ?] [? sub. ?] 01:16:32.980 --> 01:16:33.855 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:16:33.855 --> 01:16:42.700 align:middle line:90% 01:16:42.700 --> 01:16:43.200 align:middle line:90% OK. 01:16:43.200 --> 01:16:45.300 align:middle line:90% So this one has a subscript. 01:16:45.300 --> 01:16:47.560 align:middle line:84% For those of you who are not familiar with subscripts, 01:16:47.560 --> 01:16:50.140 align:middle line:84% basically they allow you to look at-- 01:16:50.140 --> 01:16:52.800 align:middle line:90% 01:16:52.800 --> 01:16:55.880 align:middle line:84% you look at any variable and have multiple copies of it. 01:16:55.880 --> 01:16:59.280 align:middle line:84% So I don't know whether it's subscripted on these. 01:16:59.280 --> 01:16:59.780 align:middle line:90% Yes. 01:16:59.780 --> 01:17:00.420 align:middle line:90% So it's-- 01:17:00.420 --> 01:17:02.020 align:middle line:84% AUDIENCE: You have no vax and a vax [? rate. ?] 01:17:02.020 --> 01:17:02.895 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:17:02.895 --> 01:17:08.020 align:middle line:84% So you have no vax and vax as your-- 01:17:08.020 --> 01:17:09.980 align:middle line:84% so this is where the subscript shows up 01:17:09.980 --> 01:17:13.820 align:middle line:90% in Vensim's user interface. 01:17:13.820 --> 01:17:15.460 align:middle line:84% And you can have separate equations 01:17:15.460 --> 01:17:20.220 align:middle line:84% or have the same equation that applies to all of the members. 01:17:20.220 --> 01:17:20.720 align:middle line:90% OK. 01:17:20.720 --> 01:17:25.430 align:middle line:84% So now again, here we have the vaccination process, 01:17:25.430 --> 01:17:29.470 align:middle line:84% so let's look at how the vaccination is formulated. 01:17:29.470 --> 01:17:34.630 align:middle line:90% So total vaxed is a sum-- 01:17:34.630 --> 01:17:36.290 align:middle line:90% AUDIENCE: It's the sum of all-- 01:17:36.290 --> 01:17:39.070 align:middle line:90% both susceptible vax and-- 01:17:39.070 --> 01:17:41.330 align:middle line:84% HAZHIR RAHMANDAD: But why not recovered vax? 01:17:41.330 --> 01:17:44.270 align:middle line:90% 01:17:44.270 --> 01:17:46.390 align:middle line:84% AUDIENCE: I think I don't have a recovered. 01:17:46.390 --> 01:17:49.350 align:middle line:84% I add them up all into the recovery. 01:17:49.350 --> 01:17:52.610 align:middle line:90% I didn't separate the recovered. 01:17:52.610 --> 01:17:55.570 align:middle line:84% HAZHIR RAHMANDAD: OK, but conceptually-- 01:17:55.570 --> 01:17:59.030 align:middle line:84% so what Hesam is trying to do is to calculate the total number 01:17:59.030 --> 01:18:01.910 align:middle line:84% of people who are vaccinated in the population, 01:18:01.910 --> 01:18:06.150 align:middle line:84% then compare that against the total population 01:18:06.150 --> 01:18:10.150 align:middle line:84% and see whether we have people left out who 01:18:10.150 --> 01:18:13.410 align:middle line:84% are not yet vaccinated, but are willing to get vaccinated. 01:18:13.410 --> 01:18:16.490 align:middle line:84% So that's the general idea you need. 01:18:16.490 --> 01:18:19.270 align:middle line:84% You calculate how many total vaccinated people 01:18:19.270 --> 01:18:21.250 align:middle line:84% versus how many are willing, which 01:18:21.250 --> 01:18:24.250 align:middle line:84% is the total population multiplied by fraction 01:18:24.250 --> 01:18:25.230 align:middle line:90% vaccinated. 01:18:25.230 --> 01:18:27.610 align:middle line:84% And then comparing those two, you 01:18:27.610 --> 01:18:30.190 align:middle line:84% get a gap, a fraction of the total-- 01:18:30.190 --> 01:18:33.130 align:middle line:84% then you turn that into a fraction of total population. 01:18:33.130 --> 01:18:37.010 align:middle line:84% That becomes out of all the rest of the population, 01:18:37.010 --> 01:18:40.650 align:middle line:84% that fraction is willing to get vaccinated. 01:18:40.650 --> 01:18:45.110 align:middle line:84% So then from your susceptible unvaccinated, 01:18:45.110 --> 01:18:47.810 align:middle line:84% you use that fraction of them only 01:18:47.810 --> 01:18:51.290 align:middle line:90% to drive the vaccination rate. 01:18:51.290 --> 01:18:53.867 align:middle line:84% AUDIENCE: Why are infections people included in that? 01:18:53.867 --> 01:18:56.450 align:middle line:84% HAZHIR RAHMANDAD: Because there are people who were vaccinated 01:18:56.450 --> 01:18:57.910 align:middle line:90% and are now infectious. 01:18:57.910 --> 01:18:59.550 align:middle line:84% You don't care about their infection. 01:18:59.550 --> 01:19:00.730 align:middle line:84% You care about the fact that they 01:19:00.730 --> 01:19:02.813 align:middle line:84% were willing to be vaccinated, and therefore, they 01:19:02.813 --> 01:19:06.050 align:middle line:90% are in the vaccinated group. 01:19:06.050 --> 01:19:09.090 align:middle line:84% Anybody has done it in a way that they think 01:19:09.090 --> 01:19:10.630 align:middle line:90% is consistent with the story? 01:19:10.630 --> 01:19:12.130 align:middle line:84% AUDIENCE: I just want to check mine. 01:19:12.130 --> 01:19:12.610 align:middle line:90% I don't know-- 01:19:12.610 --> 01:19:13.568 align:middle line:90% HAZHIR RAHMANDAD: Sure. 01:19:13.568 --> 01:19:15.590 align:middle line:90% So let's take a look at Ali's. 01:19:15.590 --> 01:19:18.140 align:middle line:90% 01:19:18.140 --> 01:19:23.100 align:middle line:84% So we have susceptible that go to vaccination rate, 01:19:23.100 --> 01:19:32.060 align:middle line:84% and then we have the susceptible fraction, fraction interested. 01:19:32.060 --> 01:19:36.660 align:middle line:90% So I'm not sure if this-- 01:19:36.660 --> 01:19:40.100 align:middle line:84% AUDIENCE: I actually did the fraction of susceptible 01:19:40.100 --> 01:19:41.540 align:middle line:90% over the population. 01:19:41.540 --> 01:19:44.120 align:middle line:84% HAZHIR RAHMANDAD: But this is over the total population. 01:19:44.120 --> 01:19:44.340 align:middle line:90% AUDIENCE: Yes. 01:19:44.340 --> 01:19:46.632 align:middle line:84% HAZHIR RAHMANDAD: So you have the susceptible fraction, 01:19:46.632 --> 01:19:49.740 align:middle line:84% but just this is very similar to the-- 01:19:49.740 --> 01:19:51.480 align:middle line:90% Russ's equation. 01:19:51.480 --> 01:19:55.980 align:middle line:90% That is, if you have the-- 01:19:55.980 --> 01:19:59.060 align:middle line:84% if you ignore all of the other things that are happening, 01:19:59.060 --> 01:20:03.260 align:middle line:84% just look at the s moving to vaccinated, 01:20:03.260 --> 01:20:06.320 align:middle line:84% that everybody from the s will move to the vaccinated. 01:20:06.320 --> 01:20:07.580 align:middle line:90% AUDIENCE: No, I hear you. 01:20:07.580 --> 01:20:13.100 align:middle line:84% So if the fraction, susceptible fraction, is-- 01:20:13.100 --> 01:20:14.160 align:middle line:90% if you can't control-- 01:20:14.160 --> 01:20:15.077 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:20:15.077 --> 01:20:18.735 align:middle line:84% So let's open the vaccination rate. 01:20:18.735 --> 01:20:20.070 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:20:20.070 --> 01:20:20.987 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:20:20.987 --> 01:20:24.600 align:middle line:84% So you're looking at the vaccine capacity multiplied 01:20:24.600 --> 01:20:26.980 align:middle line:84% by what fraction of the population-- 01:20:26.980 --> 01:20:31.520 align:middle line:84% whether the fraction of people who are susceptible 01:20:31.520 --> 01:20:34.400 align:middle line:90% are above fraction interested. 01:20:34.400 --> 01:20:36.100 align:middle line:84% So there are a couple of issues here. 01:20:36.100 --> 01:20:38.720 align:middle line:84% First of all, I'm worried about this equation 01:20:38.720 --> 01:20:43.240 align:middle line:84% because it can become negative if those fractions are not 01:20:43.240 --> 01:20:44.220 align:middle line:90% correctly matched. 01:20:44.220 --> 01:20:47.080 align:middle line:84% Now, maybe they would never happen 01:20:47.080 --> 01:20:49.560 align:middle line:84% if they are very well formulated, 01:20:49.560 --> 01:20:53.260 align:middle line:84% but it is a risk that worries me by looking at this formulation, 01:20:53.260 --> 01:20:55.600 align:middle line:84% because vaccination rates should never be negative. 01:20:55.600 --> 01:20:59.840 align:middle line:84% So thinking about this equation and not 01:20:59.840 --> 01:21:04.600 align:middle line:84% letting the robustness to be dependent on other formulations 01:21:04.600 --> 01:21:05.780 align:middle line:90% will help you. 01:21:05.780 --> 01:21:08.100 align:middle line:90% So that's a general lesson. 01:21:08.100 --> 01:21:12.400 align:middle line:84% The other then part is susceptible fraction 01:21:12.400 --> 01:21:15.810 align:middle line:84% is what fraction of population is susceptible. 01:21:15.810 --> 01:21:21.130 align:middle line:84% So that is conceptually different from fraction 01:21:21.130 --> 01:21:25.810 align:middle line:84% that is interested in getting vaccinated. 01:21:25.810 --> 01:21:31.450 align:middle line:84% So if you have a big wave of COVID, 01:21:31.450 --> 01:21:35.290 align:middle line:84% and you can't do everybody-- you can't vaccinate everybody, 01:21:35.290 --> 01:21:39.090 align:middle line:84% so everybody will get out of the susceptible population 01:21:39.090 --> 01:21:41.210 align:middle line:90% because they get sick. 01:21:41.210 --> 01:21:45.450 align:middle line:84% Susceptible fraction goes to 0, whereas fraction interested 01:21:45.450 --> 01:21:46.270 align:middle line:90% is not. 01:21:46.270 --> 01:21:50.430 align:middle line:84% And therefore, this will lead to negative numbers 01:21:50.430 --> 01:21:52.890 align:middle line:90% that shouldn't happen. 01:21:52.890 --> 01:21:55.570 align:middle line:90% So this is also not working. 01:21:55.570 --> 01:21:58.290 align:middle line:90% But let's see if-- 01:21:58.290 --> 01:22:01.030 align:middle line:90% at least the units are good. 01:22:01.030 --> 01:22:01.530 align:middle line:90% OK. 01:22:01.530 --> 01:22:04.682 align:middle line:90% [CHUCKLING] 01:22:04.682 --> 01:22:05.570 align:middle line:90% Ah. 01:22:05.570 --> 01:22:06.450 align:middle line:90% Let's see. 01:22:06.450 --> 01:22:11.410 align:middle line:84% Actually, Ann is not here-- or let's bring up-- yeah, 01:22:11.410 --> 01:22:12.110 align:middle line:90% she submitted. 01:22:12.110 --> 01:22:13.850 align:middle line:90% She has her model here. 01:22:13.850 --> 01:22:15.330 align:middle line:90% So let's open Ann's model. 01:22:15.330 --> 01:22:18.110 align:middle line:90% 01:22:18.110 --> 01:22:20.970 align:middle line:90% So this is the same problem. 01:22:20.970 --> 01:22:24.150 align:middle line:84% So it's not going to work, because basically, it 01:22:24.150 --> 01:22:28.110 align:middle line:84% is using the fraction that can be 01:22:28.110 --> 01:22:33.390 align:middle line:84% vaccinated, willing to vaccinate going to the multiplied 01:22:33.390 --> 01:22:34.330 align:middle line:90% by susceptible. 01:22:34.330 --> 01:22:34.830 align:middle line:90% Same issue. 01:22:34.830 --> 01:22:36.122 align:middle line:90% AUDIENCE: Can I ask a question? 01:22:36.122 --> 01:22:38.030 align:middle line:84% In my formulation, if I had defined 01:22:38.030 --> 01:22:41.070 align:middle line:84% the fraction interested as a function 01:22:41.070 --> 01:22:43.190 align:middle line:84% of the total population, wouldn't that 01:22:43.190 --> 01:22:45.110 align:middle line:90% solve the negativity issue? 01:22:45.110 --> 01:22:47.310 align:middle line:84% HAZHIR RAHMANDAD: So if it was as a function 01:22:47.310 --> 01:22:50.790 align:middle line:90% of the total population? 01:22:50.790 --> 01:22:54.190 align:middle line:90% So let's bring it back up. 01:22:54.190 --> 01:22:55.530 align:middle line:90% What do you mean? 01:22:55.530 --> 01:22:57.770 align:middle line:84% Oh, not the formulation you currently have. 01:22:57.770 --> 01:23:00.570 align:middle line:84% You're thinking about a fraction interest, that that would be-- 01:23:00.570 --> 01:23:01.550 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:23:01.550 --> 01:23:01.750 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:23:01.750 --> 01:23:02.710 align:middle line:90% Yeah. 01:23:02.710 --> 01:23:04.850 align:middle line:90% Mmm, It's going to be tough. 01:23:04.850 --> 01:23:06.990 align:middle line:84% I don't like to change the fraction 01:23:06.990 --> 01:23:09.028 align:middle line:90% interested from a constant. 01:23:09.028 --> 01:23:10.570 align:middle line:84% I want it to be a constant because it 01:23:10.570 --> 01:23:11.590 align:middle line:90% is a well-defined thing. 01:23:11.590 --> 01:23:13.250 align:middle line:84% You can say, OK, this population we 01:23:13.250 --> 01:23:15.650 align:middle line:84% have surveyed suggest there are 80% interested, 01:23:15.650 --> 01:23:19.530 align:middle line:90% or 90% interested, or so on. 01:23:19.530 --> 01:23:22.090 align:middle line:90% So keep that, whatever it is. 01:23:22.090 --> 01:23:23.890 align:middle line:84% The way you need to actually tackle 01:23:23.890 --> 01:23:29.410 align:middle line:84% this is to calculate the total number of people 01:23:29.410 --> 01:23:36.050 align:middle line:84% who are vaccinated, compare that with the total population. 01:23:36.050 --> 01:23:38.050 align:middle line:84% You get to a fraction that is currently 01:23:38.050 --> 01:23:43.890 align:middle line:84% vaccinated versus the fraction that is maximum fraction that 01:23:43.890 --> 01:23:47.290 align:middle line:90% is willing to be vaccinated. 01:23:47.290 --> 01:23:50.130 align:middle line:90% So it might be 5%. 01:23:50.130 --> 01:23:54.650 align:middle line:84% That gap is the fraction of the rest 01:23:54.650 --> 01:23:59.010 align:middle line:84% of the population who are still willing to get vaccinated. 01:23:59.010 --> 01:24:03.490 align:middle line:84% So use that gap, that fraction, to multiply it 01:24:03.490 --> 01:24:06.490 align:middle line:90% by the susceptible population. 01:24:06.490 --> 01:24:09.500 align:middle line:84% So the susceptible unvaccinated, the fraction 01:24:09.500 --> 01:24:12.260 align:middle line:84% of those who are willing to get vaccinated 01:24:12.260 --> 01:24:14.120 align:middle line:90% is that gap between the two. 01:24:14.120 --> 01:24:18.220 align:middle line:90% So is the logic clear? 01:24:18.220 --> 01:24:19.700 align:middle line:90% Question, Cathy? 01:24:19.700 --> 01:24:22.860 align:middle line:84% AUDIENCE: Can you do it without-- so the way I did it-- 01:24:22.860 --> 01:24:24.360 align:middle line:84% can you do it without the fractions? 01:24:24.360 --> 01:24:28.460 align:middle line:84% The way that I did it was just having the gap of-- 01:24:28.460 --> 01:24:30.160 align:middle line:84% the gap is in the units of people. 01:24:30.160 --> 01:24:32.580 align:middle line:84% HAZHIR RAHMANDAD: OK, let's look at your model. 01:24:32.580 --> 01:24:34.235 align:middle line:90% AUDIENCE: Frequency model. 01:24:34.235 --> 01:24:34.860 align:middle line:90% AUDIENCE: Yeah. 01:24:34.860 --> 01:24:38.380 align:middle line:90% Yeah, [? frequency ?] model. 01:24:38.380 --> 01:24:41.343 align:middle line:84% And then it's capacity constraint that I don't think-- 01:24:41.343 --> 01:24:43.260 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so capacity constraint 01:24:43.260 --> 01:24:44.440 align:middle line:90% is more straightforward. 01:24:44.440 --> 01:24:46.780 align:middle line:84% This is kind of the more challenging part 01:24:46.780 --> 01:24:48.380 align:middle line:90% of the formulation. 01:24:48.380 --> 01:24:52.540 align:middle line:84% AUDIENCE: So this is all up in the upper right. 01:24:52.540 --> 01:24:55.820 align:middle line:84% HAZHIR RAHMANDAD: So you have the vaccinated population. 01:24:55.820 --> 01:25:02.380 align:middle line:84% And then the vaccination rate is-- let's-- 01:25:02.380 --> 01:25:05.900 align:middle line:84% AUDIENCE: On the upper right of the screen. 01:25:05.900 --> 01:25:06.500 align:middle line:90% Scroll up. 01:25:06.500 --> 01:25:08.520 align:middle line:84% HAZHIR RAHMANDAD: Oh, do you have formulated it up there. 01:25:08.520 --> 01:25:09.145 align:middle line:90% AUDIENCE: Yeah. 01:25:09.145 --> 01:25:10.200 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:25:10.200 --> 01:25:14.420 align:middle line:84% So effective capacity utilization. 01:25:14.420 --> 01:25:17.440 align:middle line:90% 01:25:17.440 --> 01:25:19.880 align:middle line:84% AUDIENCE: So that's just a fuzzy min. 01:25:19.880 --> 01:25:25.360 align:middle line:84% HAZHIR RAHMANDAD: Yeah, but this is all about capacity. 01:25:25.360 --> 01:25:27.320 align:middle line:84% So then we have to really figure out 01:25:27.320 --> 01:25:30.713 align:middle line:84% what is the indicated capacity utilization, correct? 01:25:30.713 --> 01:25:31.880 align:middle line:90% AUDIENCE: Yeah, [INAUDIBLE]. 01:25:31.880 --> 01:25:33.380 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:25:33.380 --> 01:25:38.565 align:middle line:90% 01:25:38.565 --> 01:25:41.220 align:middle line:84% And this is about indicated vaccination rate, 01:25:41.220 --> 01:25:43.840 align:middle line:84% so we need to figure out the indicated vaccination 01:25:43.840 --> 01:25:52.000 align:middle line:84% rate, which is coming from the vaccinated population 01:25:52.000 --> 01:25:54.820 align:middle line:90% versus indicated vaccinated. 01:25:54.820 --> 01:25:56.660 align:middle line:90% So this is OK. 01:25:56.660 --> 01:26:00.480 align:middle line:84% This is a good calculation that is-- so what Cathy is doing here 01:26:00.480 --> 01:26:04.040 align:middle line:84% is looking at the indicated vaccinated population that 01:26:04.040 --> 01:26:06.890 align:middle line:84% is the total number willing to get vaccinated 01:26:06.890 --> 01:26:09.190 align:middle line:84% versus the current vaccinated population. 01:26:09.190 --> 01:26:14.290 align:middle line:90% Now, how is this one calculated? 01:26:14.290 --> 01:26:19.890 align:middle line:84% This is actually the stock of total vaccinated population. 01:26:19.890 --> 01:26:20.510 align:middle line:90% I see. 01:26:20.510 --> 01:26:21.170 align:middle line:90% I see. 01:26:21.170 --> 01:26:23.970 align:middle line:84% So in this model, the way Cathy is 01:26:23.970 --> 01:26:27.690 align:middle line:84% dealing with vaccinated people is that they don't get sick-- 01:26:27.690 --> 01:26:28.990 align:middle line:90% well, they do get sick. 01:26:28.990 --> 01:26:30.290 align:middle line:90% AUDIENCE: They get sick. 01:26:30.290 --> 01:26:32.450 align:middle line:84% HAZHIR RAHMANDAD: Ah, so then what wouldn't work. 01:26:32.450 --> 01:26:36.370 align:middle line:84% So if these people get vaccinated, 01:26:36.370 --> 01:26:40.410 align:middle line:84% and then they get sick, in your calculus, 01:26:40.410 --> 01:26:43.570 align:middle line:84% they are back into the main stock and flow chain. 01:26:43.570 --> 01:26:46.130 align:middle line:84% They are now into the infectious population. 01:26:46.130 --> 01:26:47.810 align:middle line:84% And you have lost track of whether they 01:26:47.810 --> 01:26:50.908 align:middle line:90% were vaccinated or not. 01:26:50.908 --> 01:26:51.450 align:middle line:90% AUDIENCE: OK. 01:26:51.450 --> 01:26:51.950 align:middle line:90% Yeah. 01:26:51.950 --> 01:26:56.190 align:middle line:84% So I was thinking about-- in terms of-- 01:26:56.190 --> 01:26:56.690 align:middle line:90% right. 01:26:56.690 --> 01:27:00.530 align:middle line:84% So I think partly, I'm tracking whether they're 01:27:00.530 --> 01:27:02.778 align:middle line:84% vaccinated and subscripts for the recovery. 01:27:02.778 --> 01:27:04.570 align:middle line:84% HAZHIR RAHMANDAD: You have subscripts here? 01:27:04.570 --> 01:27:04.990 align:middle line:90% AUDIENCE: Yeah. 01:27:04.990 --> 01:27:06.032 align:middle line:90% HAZHIR RAHMANDAD: Oh, OK. 01:27:06.032 --> 01:27:07.830 align:middle line:84% AUDIENCE: So I think if what you mean 01:27:07.830 --> 01:27:10.697 align:middle line:84% is that they become as if they were never vaccinated? 01:27:10.697 --> 01:27:12.530 align:middle line:84% HAZHIR RAHMANDAD: So that's a good question. 01:27:12.530 --> 01:27:17.310 align:middle line:84% I mean, if you have subscripts, you can track that. 01:27:17.310 --> 01:27:21.590 align:middle line:84% So the vaccinated infectious population 01:27:21.590 --> 01:27:24.870 align:middle line:84% is vaccinated infection, rate recovery rate for vaccinated, 01:27:24.870 --> 01:27:25.810 align:middle line:90% this rate vaccinated. 01:27:25.810 --> 01:27:27.290 align:middle line:90% So then you can track that. 01:27:27.290 --> 01:27:28.230 align:middle line:90% That's good. 01:27:28.230 --> 01:27:34.550 align:middle line:84% But then in your equation up here for vaccinated population 01:27:34.550 --> 01:27:38.070 align:middle line:84% V, it is actually not just the people who are vaccinated 01:27:38.070 --> 01:27:40.590 align:middle line:90% but are not sick or recovered. 01:27:40.590 --> 01:27:45.670 align:middle line:84% It is also all of the sick and recovered vaccinated people who 01:27:45.670 --> 01:27:48.110 align:middle line:84% should be counted towards creating 01:27:48.110 --> 01:27:55.070 align:middle line:84% that indicated vaccination rate, or to some gap variable. 01:27:55.070 --> 01:28:00.200 align:middle line:84% AUDIENCE: I was thinking that once you're sick, 01:28:00.200 --> 01:28:04.480 align:middle line:84% it doesn't matter if you were previously vaccinated, and then, 01:28:04.480 --> 01:28:05.160 align:middle line:90% like the vax-- 01:28:05.160 --> 01:28:06.620 align:middle line:84% HAZHIR RAHMANDAD: It doesn't matter for what? 01:28:06.620 --> 01:28:08.920 align:middle line:84% AUDIENCE: It doesn't matter for-- you would still 01:28:08.920 --> 01:28:12.562 align:middle line:84% decide in six months, I want to get vaccinated again. 01:28:12.562 --> 01:28:13.520 align:middle line:90% HAZHIR RAHMANDAD: Sure. 01:28:13.520 --> 01:28:15.620 align:middle line:84% You want to get vaccinated again. 01:28:15.620 --> 01:28:18.280 align:middle line:84% But here, what you're trying to calculate 01:28:18.280 --> 01:28:22.600 align:middle line:84% is how many people are left willing to get vaccinated, 01:28:22.600 --> 01:28:25.320 align:middle line:90% but not yet vaccinated. 01:28:25.320 --> 01:28:27.320 align:middle line:90% The second part is important. 01:28:27.320 --> 01:28:29.960 align:middle line:84% The ones who are already vaccinated, and their vaccine 01:28:29.960 --> 01:28:33.880 align:middle line:84% has not waned, and are willing to be vaccinated 01:28:33.880 --> 01:28:37.280 align:middle line:84% should be deducted from the total number 01:28:37.280 --> 01:28:41.000 align:middle line:84% of people who are willing to be vaccinated 01:28:41.000 --> 01:28:42.460 align:middle line:90% in the total population. 01:28:42.460 --> 01:28:45.400 align:middle line:84% So let's say I have 100 people in the population, 80 of them 01:28:45.400 --> 01:28:47.180 align:middle line:90% are willing to get vaccinated. 01:28:47.180 --> 01:28:52.640 align:middle line:84% Out of this 80 people, 50 of them are in your vaccinated-- 01:28:52.640 --> 01:28:55.240 align:middle line:90% in the vaccinated population. 01:28:55.240 --> 01:28:58.780 align:middle line:84% Now I have 30 people in other are stocks, 01:28:58.780 --> 01:29:00.900 align:middle line:84% in the stock of infected vaccinated 01:29:00.900 --> 01:29:04.140 align:middle line:84% and recovered vaccinated, who are not 01:29:04.140 --> 01:29:06.940 align:middle line:90% willing to get vaccinated. 01:29:06.940 --> 01:29:11.740 align:middle line:84% So the indicated vaccination rate I would get 01:29:11.740 --> 01:29:20.020 align:middle line:84% needs to only look at anybody out of the 80 01:29:20.020 --> 01:29:23.260 align:middle line:90% who is not yet vaccinated. 01:29:23.260 --> 01:29:29.380 align:middle line:84% But you're taking out 50 of them, but not the other 30, 01:29:29.380 --> 01:29:30.720 align:middle line:90% and that makes it harder. 01:29:30.720 --> 01:29:36.600 align:middle line:84% Now, this indicated vaccination rate-- and it's kind of a-- 01:29:36.600 --> 01:29:37.100 align:middle line:90% good. 01:29:37.100 --> 01:29:43.880 align:middle line:84% Your units are-- so this is more complex formulation. 01:29:43.880 --> 01:29:50.900 align:middle line:84% So you have the V gap divided by time 01:29:50.900 --> 01:29:58.470 align:middle line:84% to close the gap plus vaccinated infection rate 01:29:58.470 --> 01:30:02.830 align:middle line:90% plus vaccination waning rate. 01:30:02.830 --> 01:30:07.050 align:middle line:84% So you are saying as soon as somebody is infected, 01:30:07.050 --> 01:30:09.630 align:middle line:84% somebody who is vaccinated is infected, 01:30:09.630 --> 01:30:13.434 align:middle line:90% you want them to get vaccinated. 01:30:13.434 --> 01:30:14.812 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:30:14.812 --> 01:30:17.270 align:middle line:84% HAZHIR RAHMANDAD: Because this is the indicated vaccination 01:30:17.270 --> 01:30:17.770 align:middle line:90% rate. 01:30:17.770 --> 01:30:20.270 align:middle line:84% Now, assuming there is no capacity limits. 01:30:20.270 --> 01:30:22.830 align:middle line:84% AUDIENCE: Yeah, I want somebody to get vaccinated. 01:30:22.830 --> 01:30:24.205 align:middle line:84% HAZHIR RAHMANDAD: You want some-- 01:30:24.205 --> 01:30:25.590 align:middle line:90% AUDIENCE: Infected people? 01:30:25.590 --> 01:30:30.390 align:middle line:84% HAZHIR RAHMANDAD: As soon as somebody infected becomes-- 01:30:30.390 --> 01:30:32.835 align:middle line:84% gets infected, somebody vaccinated gets infected, 01:30:32.835 --> 01:30:34.210 align:middle line:84% you want somebody-- you're right. 01:30:34.210 --> 01:30:37.030 align:middle line:84% You want somebody to get vaccinated. 01:30:37.030 --> 01:30:39.470 align:middle line:90% What's the logic for that? 01:30:39.470 --> 01:30:44.530 align:middle line:84% AUDIENCE: Well, I think I was just doing the stock control 01:30:44.530 --> 01:30:47.510 align:middle line:90% [? towards ?] that problem. 01:30:47.510 --> 01:30:50.270 align:middle line:84% HAZHIR RAHMANDAD: Yes, but this is not exactly the stock control 01:30:50.270 --> 01:30:51.530 align:middle line:90% that you are trying to do. 01:30:51.530 --> 01:30:54.010 align:middle line:84% This is kind of a little bit of a-- 01:30:54.010 --> 01:30:57.030 align:middle line:84% I don't know what is happening exactly here, 01:30:57.030 --> 01:30:59.690 align:middle line:84% but you're saying as soon as somebody 01:30:59.690 --> 01:31:04.930 align:middle line:84% gets the disease, somebody else in the unvaccinated population, 01:31:04.930 --> 01:31:06.345 align:middle line:90% you are going to vaccinate them. 01:31:06.345 --> 01:31:06.970 align:middle line:90% AUDIENCE: Yeah. 01:31:06.970 --> 01:31:10.330 align:middle line:84% I think my-- the thread of thought 01:31:10.330 --> 01:31:15.810 align:middle line:84% here is that once somebody is infected, it doesn't matter. 01:31:15.810 --> 01:31:18.170 align:middle line:84% I mean, it matters for the death versus recovery, 01:31:18.170 --> 01:31:20.010 align:middle line:84% but otherwise, it doesn't matter if they 01:31:20.010 --> 01:31:23.830 align:middle line:84% were vaccinated before because they got infected anyways. 01:31:23.830 --> 01:31:27.157 align:middle line:84% So they're kind of back in the pool of everybody. 01:31:27.157 --> 01:31:29.490 align:middle line:84% HAZHIR RAHMANDAD: So they are back in the pool of people 01:31:29.490 --> 01:31:31.850 align:middle line:84% to be vaccinated, but they are not 01:31:31.850 --> 01:31:33.310 align:middle line:90% back in the pool of everybody. 01:31:33.310 --> 01:31:34.385 align:middle line:90% So that's the problem. 01:31:34.385 --> 01:31:35.510 align:middle line:90% That's one of the problems. 01:31:35.510 --> 01:31:40.730 align:middle line:84% So this flow ultimately is draining 01:31:40.730 --> 01:31:44.250 align:middle line:84% people who are susceptible and taking them 01:31:44.250 --> 01:31:46.410 align:middle line:90% to the vaccinated population. 01:31:46.410 --> 01:31:49.090 align:middle line:84% But once somebody gets infected, they 01:31:49.090 --> 01:31:51.350 align:middle line:84% are not in the susceptible population. 01:31:51.350 --> 01:31:53.320 align:middle line:84% They are in the infectious population. 01:31:53.320 --> 01:31:57.060 align:middle line:84% So this could lead to rates of vaccination 01:31:57.060 --> 01:31:59.920 align:middle line:84% that exceeds the available susceptible population. 01:31:59.920 --> 01:32:03.960 align:middle line:84% So it is very important not to even go down that road. 01:32:03.960 --> 01:32:07.000 align:middle line:84% That creates all kinds of messy problems. 01:32:07.000 --> 01:32:10.100 align:middle line:84% But all of the problems start with lack of clarity 01:32:10.100 --> 01:32:11.360 align:middle line:90% on the underlying mechanism. 01:32:11.360 --> 01:32:13.900 align:middle line:84% So the mechanism is not that when I get sick, 01:32:13.900 --> 01:32:18.300 align:middle line:84% or if I recover, somebody else should get vaccinated 01:32:18.300 --> 01:32:20.300 align:middle line:90% from the susceptible group. 01:32:20.300 --> 01:32:23.420 align:middle line:84% You should let these people-- to go back into the susceptible 01:32:23.420 --> 01:32:27.420 align:middle line:84% group with waning of immunity and waning of vaccination, 01:32:27.420 --> 01:32:30.460 align:middle line:84% they could go into the-- being a susceptible who 01:32:30.460 --> 01:32:32.700 align:middle line:84% is in need of vaccination, and then 01:32:32.700 --> 01:32:35.120 align:middle line:84% get them vaccinated with whatever rate you want. 01:32:35.120 --> 01:32:38.578 align:middle line:84% So from that group, you take them out. 01:32:38.578 --> 01:32:39.120 align:middle line:90% AUDIENCE: OK. 01:32:39.120 --> 01:32:43.620 align:middle line:84% So resolving this would be taking out those correction-- 01:32:43.620 --> 01:32:45.700 align:middle line:84% quote unquote "corrections," that I tried to-- 01:32:45.700 --> 01:32:47.980 align:middle line:84% HAZHIR RAHMANDAD: Yeah, those definitely need to go. 01:32:47.980 --> 01:32:53.960 align:middle line:84% Then you need to have the vaccination waning 01:32:53.960 --> 01:32:56.160 align:middle line:84% rate to not be vaccinated-- sorry 01:32:56.160 --> 01:32:57.420 align:middle line:90% not vaccination waning rate. 01:32:57.420 --> 01:33:01.820 align:middle line:84% This V gap to not only be based on vaccinated population, 01:33:01.820 --> 01:33:06.020 align:middle line:84% but also other vaccinated groups that are infected 01:33:06.020 --> 01:33:08.480 align:middle line:84% vaccinated and recovered vaccinated. 01:33:08.480 --> 01:33:12.480 align:middle line:84% So that way, you can calculate a V gap, which is good. 01:33:12.480 --> 01:33:16.080 align:middle line:84% Then you divide that V gap by total population. 01:33:16.080 --> 01:33:23.400 align:middle line:84% You get the fraction of the population 01:33:23.400 --> 01:33:28.100 align:middle line:84% that is not vaccinated, but willing to be vaccinated. 01:33:28.100 --> 01:33:30.080 align:middle line:84% That's the thing that you really need, 01:33:30.080 --> 01:33:33.160 align:middle line:84% fraction that is willing to get vaccinated, but is not 01:33:33.160 --> 01:33:35.000 align:middle line:90% currently vaccinated. 01:33:35.000 --> 01:33:38.760 align:middle line:84% Then you take that fraction and use it 01:33:38.760 --> 01:33:43.840 align:middle line:84% on the susceptible population that is not vaccinated. 01:33:43.840 --> 01:33:47.080 align:middle line:84% And you say that fraction of the susceptible population 01:33:47.080 --> 01:33:52.370 align:middle line:84% is going to be open to vaccination. 01:33:52.370 --> 01:33:54.250 align:middle line:84% And that becomes the population that you 01:33:54.250 --> 01:33:56.510 align:middle line:90% drain through vaccination. 01:33:56.510 --> 01:33:57.743 align:middle line:90% Hesam? 01:33:57.743 --> 01:33:59.910 align:middle line:84% AUDIENCE: Can you take a look at my population here. 01:33:59.910 --> 01:34:03.490 align:middle line:84% I think I missed out on the vaccinated recovery 01:34:03.490 --> 01:34:04.803 align:middle line:90% population [INAUDIBLE]. 01:34:04.803 --> 01:34:06.970 align:middle line:84% HAZHIR RAHMANDAD: Yes, but other than that, we can-- 01:34:06.970 --> 01:34:08.930 align:middle line:84% AUDIENCE: That's the question-- because I wasn't sure of what 01:34:08.930 --> 01:34:10.110 align:middle line:90% I was doing myself. 01:34:10.110 --> 01:34:11.027 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:34:11.027 --> 01:34:15.935 align:middle line:90% 01:34:15.935 --> 01:34:16.842 align:middle line:90% AUDIENCE: [INAUDIBLE] 01:34:16.842 --> 01:34:18.550 align:middle line:84% HAZHIR RAHMANDAD: Yes, so the total vax-- 01:34:18.550 --> 01:34:20.210 align:middle line:90% AUDIENCE: Needed a recovered-- 01:34:20.210 --> 01:34:22.460 align:middle line:84% HAZHIR RAHMANDAD: Yes, it needs to have the recovered. 01:34:22.460 --> 01:34:23.910 align:middle line:90% But other than that, it is OK. 01:34:23.910 --> 01:34:24.490 align:middle line:90% Good. 01:34:24.490 --> 01:34:29.570 align:middle line:84% So then we have the total vaxed, and then we have-- 01:34:29.570 --> 01:34:32.670 align:middle line:84% so this formulation has five inputs into it, 01:34:32.670 --> 01:34:34.690 align:middle line:84% so it makes me a little bit anxious. 01:34:34.690 --> 01:34:38.190 align:middle line:84% Just kind of it may become messy to understand. 01:34:38.190 --> 01:34:42.890 align:middle line:84% And then it has two mean functions that will kill us. 01:34:42.890 --> 01:34:45.690 align:middle line:90% For now, let's ignore capacity. 01:34:45.690 --> 01:34:47.750 align:middle line:90% So that's easy to do. 01:34:47.750 --> 01:34:51.250 align:middle line:84% Then you have the minimum of susceptible population 01:34:51.250 --> 01:34:56.750 align:middle line:84% and interested in vax minus total vaxed divided 01:34:56.750 --> 01:34:58.250 align:middle line:90% by time to vax. 01:34:58.250 --> 01:34:59.230 align:middle line:90% So this is-- 01:34:59.230 --> 01:34:59.950 align:middle line:84% AUDIENCE: [INAUDIBLE] just a unit. 01:34:59.950 --> 01:35:01.242 align:middle line:90% HAZHIR RAHMANDAD: Yeah, I know. 01:35:01.242 --> 01:35:04.710 align:middle line:84% So this is closer, but it is still problematic. 01:35:04.710 --> 01:35:07.730 align:middle line:84% So can anybody tell what's the problem here? 01:35:07.730 --> 01:35:16.990 align:middle line:90% 01:35:16.990 --> 01:35:19.590 align:middle line:84% So what Hesam is trying to do is saying 01:35:19.590 --> 01:35:22.390 align:middle line:84% we have a number of people interested 01:35:22.390 --> 01:35:25.910 align:middle line:84% in vax minus total vax that are interested in getting 01:35:25.910 --> 01:35:28.710 align:middle line:84% vaccinated, because the interested in vax is 01:35:28.710 --> 01:35:30.190 align:middle line:84% the total number of population that 01:35:30.190 --> 01:35:31.690 align:middle line:90% is interested in vaccination. 01:35:31.690 --> 01:35:33.515 align:middle line:84% Those that are vaxed already have vaccine, 01:35:33.515 --> 01:35:34.890 align:middle line:84% this is the remaining population. 01:35:34.890 --> 01:35:36.870 align:middle line:90% This is the group we want. 01:35:36.870 --> 01:35:38.590 align:middle line:84% And it says, OK, we want to drain 01:35:38.590 --> 01:35:42.770 align:middle line:84% that group with some fractional rates-- time to vax. 01:35:42.770 --> 01:35:46.530 align:middle line:84% So we get those out of the susceptible population, 01:35:46.530 --> 01:35:52.010 align:middle line:84% except that we don't want it to overflow-- 01:35:52.010 --> 01:35:54.470 align:middle line:84% we don't want it to be bigger than susceptible population. 01:35:54.470 --> 01:35:58.350 align:middle line:84% So if the susceptible population is smaller than that gap, 01:35:58.350 --> 01:36:01.550 align:middle line:84% it would shut down to whatever susceptible population is. 01:36:01.550 --> 01:36:06.530 align:middle line:84% And if susceptible population is 0, it would not drain anything. 01:36:06.530 --> 01:36:08.050 align:middle line:90% So what's the problem. 01:36:08.050 --> 01:36:10.770 align:middle line:84% AUDIENCE: Are you saying everyone in that case, 01:36:10.770 --> 01:36:15.007 align:middle line:84% the susceptible population is smaller than that gap, 01:36:15.007 --> 01:36:17.090 align:middle line:84% you're assuming all of them want to be vaccinated. 01:36:17.090 --> 01:36:18.630 align:middle line:84% HAZHIR RAHMANDAD: To get vaccinated. 01:36:18.630 --> 01:36:19.130 align:middle line:90% Yes. 01:36:19.130 --> 01:36:21.510 align:middle line:84% So the problem is what Jason said. 01:36:21.510 --> 01:36:26.770 align:middle line:84% That is, if the minimum is the susceptible population, that is, 01:36:26.770 --> 01:36:29.050 align:middle line:84% you have a lot of unvaccinated people 01:36:29.050 --> 01:36:31.850 align:middle line:84% who are willing to get vaccinated, 01:36:31.850 --> 01:36:33.570 align:middle line:84% they may be still a small fraction 01:36:33.570 --> 01:36:35.610 align:middle line:90% of the total population. 01:36:35.610 --> 01:36:38.610 align:middle line:84% But you are draining all of the susceptible population 01:36:38.610 --> 01:36:42.050 align:middle line:90% with your rate of vaccine. 01:36:42.050 --> 01:36:44.580 align:middle line:84% For those people, they might be only 10% 01:36:44.580 --> 01:36:46.620 align:middle line:84% likely to accept vaccination, but you're 01:36:46.620 --> 01:36:48.840 align:middle line:84% assuming everybody is going to accept vaccination. 01:36:48.840 --> 01:36:51.740 align:middle line:84% Now, you wouldn't have problems with running 01:36:51.740 --> 01:36:53.760 align:middle line:84% too many people totally vaccinated, 01:36:53.760 --> 01:36:56.660 align:middle line:84% but the speed of vaccination would be unfairly high. 01:36:56.660 --> 01:36:57.980 align:middle line:90% That's the problem. 01:36:57.980 --> 01:37:00.380 align:middle line:84% Is that clear what happened here? 01:37:00.380 --> 01:37:02.560 align:middle line:84% OK, so I think it's a good time to take a break. 01:37:02.560 --> 01:37:04.720 align:middle line:90% We have had enough pressure. 01:37:04.720 --> 01:37:10.180 align:middle line:84% So 10 minutes, and then we come back. 01:37:10.180 --> 01:37:11.840 align:middle line:84% We do a few more of these and then-- 01:37:11.840 --> 01:37:15.860 align:middle line:90% 01:37:15.860 --> 01:37:17.940 align:middle line:84% So I think actually we went through quite 01:37:17.940 --> 01:37:21.560 align:middle line:84% a few of the models quickly for this vaccination question. 01:37:21.560 --> 01:37:23.580 align:middle line:84% So let me actually record those so 01:37:23.580 --> 01:37:28.320 align:middle line:84% that we know we have discussed them a little bit. 01:37:28.320 --> 01:37:43.720 align:middle line:90% 01:37:43.720 --> 01:37:49.240 align:middle line:84% OK, so we have a few of them now noted. 01:37:49.240 --> 01:37:52.360 align:middle line:84% Who else wants to look at their models? 01:37:52.360 --> 01:37:57.080 align:middle line:84% We have a little bit more time for going through this. 01:37:57.080 --> 01:38:01.400 align:middle line:84% Gerardo, do you want us to take a look at your model? 01:38:01.400 --> 01:38:04.880 align:middle line:84% AUDIENCE: [INAUDIBLE], but I just worked 01:38:04.880 --> 01:38:08.040 align:middle line:84% on the first part of the model, part A. 01:38:08.040 --> 01:38:11.860 align:middle line:84% And I think that I have to do some improvement [INAUDIBLE]. 01:38:11.860 --> 01:38:14.120 align:middle line:84% But if you want [INAUDIBLE], you can just 01:38:14.120 --> 01:38:19.600 align:middle line:84% open and try to see something about it. 01:38:19.600 --> 01:38:20.760 align:middle line:90% HAZHIR RAHMANDAD: Sure. 01:38:20.760 --> 01:38:27.240 align:middle line:90% Let's open that again. 01:38:27.240 --> 01:38:31.960 align:middle line:84% Today we are not doing that much on the analysis of the model, 01:38:31.960 --> 01:38:37.280 align:middle line:84% but that does become a very important-- 01:38:37.280 --> 01:38:40.490 align:middle line:84% so you have a big risk perception structure, 01:38:40.490 --> 01:38:45.090 align:middle line:84% and then you have the basic SIR model another view, 01:38:45.090 --> 01:38:48.490 align:middle line:84% and then the risk perception goes into current contact 01:38:48.490 --> 01:38:50.490 align:middle line:90% rate and current infectivity. 01:38:50.490 --> 01:38:54.410 align:middle line:84% So let's take a look at your risk perception sector. 01:38:54.410 --> 01:39:02.410 align:middle line:84% You're saying that we get started with the infection rate. 01:39:02.410 --> 01:39:06.690 align:middle line:84% Then this is creates a reference infection rate. 01:39:06.690 --> 01:39:10.050 align:middle line:84% And you also get a reference death rate, which is basically 01:39:10.050 --> 01:39:12.990 align:middle line:90% delays or smooth functions. 01:39:12.990 --> 01:39:16.170 align:middle line:90% 01:39:16.170 --> 01:39:22.230 align:middle line:84% And you turn that into some risk perception. 01:39:22.230 --> 01:39:23.470 align:middle line:90% How does that work? 01:39:23.470 --> 01:39:28.890 align:middle line:90% 01:39:28.890 --> 01:39:30.190 align:middle line:90% So ah, interesting. 01:39:30.190 --> 01:39:35.010 align:middle line:84% So you're saying that people adjust their tolerance for risk 01:39:35.010 --> 01:39:39.550 align:middle line:84% based on recent infection rate and death. 01:39:39.550 --> 01:39:44.290 align:middle line:84% So folks, notice in the other models we have been using, 01:39:44.290 --> 01:39:46.630 align:middle line:84% we have had these reference infection rate and reference 01:39:46.630 --> 01:39:50.350 align:middle line:84% death rates, or equivalents of those, that says, 01:39:50.350 --> 01:39:51.450 align:middle line:90% how do you normalize? 01:39:51.450 --> 01:39:54.350 align:middle line:84% How do you decide if this is a high level or low level? 01:39:54.350 --> 01:39:56.990 align:middle line:84% And we have had them as a constant. 01:39:56.990 --> 01:40:02.290 align:middle line:84% What Gerardo is doing is saying, oh, actually, 01:40:02.290 --> 01:40:07.510 align:middle line:84% let's make these endogenous with some-- that is basically 01:40:07.510 --> 01:40:11.030 align:middle line:84% over a longer time horizon, you change your norm 01:40:11.030 --> 01:40:14.830 align:middle line:84% and you get used to basically the current rate of death. 01:40:14.830 --> 01:40:21.510 align:middle line:84% But the adjustment time for that reference here is one day, 01:40:21.510 --> 01:40:26.030 align:middle line:84% and I guess not very long here either. 01:40:26.030 --> 01:40:27.990 align:middle line:90% And then one day here. 01:40:27.990 --> 01:40:30.490 align:middle line:84% AUDIENCE: So it does not focus so much on the parameter. 01:40:30.490 --> 01:40:34.120 align:middle line:84% But the idea is that basically, people 01:40:34.120 --> 01:40:39.600 align:middle line:84% can adjust their thoughts based on what is happening in the-- 01:40:39.600 --> 01:40:41.600 align:middle line:84% HAZHIR RAHMANDAD: Yes, but adjust their thoughts 01:40:41.600 --> 01:40:43.340 align:middle line:90% about what is very important. 01:40:43.340 --> 01:40:47.500 align:middle line:84% So the way I saw this, at least at the beginning, was OK, 01:40:47.500 --> 01:40:49.240 align:middle line:84% you have your infection rate, but you 01:40:49.240 --> 01:40:52.300 align:middle line:84% need to decide whether this is a high number or a low number. 01:40:52.300 --> 01:40:54.800 align:middle line:84% You compare that with a baseline, which is 01:40:54.800 --> 01:40:56.520 align:middle line:90% your reference infection rate. 01:40:56.520 --> 01:41:00.600 align:middle line:84% And using that, you may say now we have high levels of infection 01:41:00.600 --> 01:41:03.560 align:middle line:84% and that means more responsiveness or less. 01:41:03.560 --> 01:41:05.420 align:middle line:90% And that is logically correct. 01:41:05.420 --> 01:41:07.240 align:middle line:90% It's kind of in the right space. 01:41:07.240 --> 01:41:09.100 align:middle line:90% I'm OK with that. 01:41:09.100 --> 01:41:10.800 align:middle line:84% And I'm OK with the idea that people 01:41:10.800 --> 01:41:13.400 align:middle line:84% adjust that reference point because, yeah, you 01:41:13.400 --> 01:41:16.220 align:middle line:84% get used to things and your standards change. 01:41:16.220 --> 01:41:20.260 align:middle line:84% If today, we see 1,000 deaths from COVID in one day, 01:41:20.260 --> 01:41:22.920 align:middle line:84% it would be a very different emotional reaction compared 01:41:22.920 --> 01:41:26.180 align:middle line:84% to when at the height of the pandemic, 01:41:26.180 --> 01:41:29.160 align:middle line:84% we might have had 3,000 deaths per day. 01:41:29.160 --> 01:41:33.860 align:middle line:84% So all of that makes sense, except that the time constants 01:41:33.860 --> 01:41:37.660 align:middle line:84% for these reference adjustments are not 01:41:37.660 --> 01:41:39.540 align:middle line:84% in the order of one day or two day. 01:41:39.540 --> 01:41:42.000 align:middle line:84% These are in the order of hundreds of days. 01:41:42.000 --> 01:41:46.820 align:middle line:84% That is, people don't get used to death or infection 01:41:46.820 --> 01:41:49.080 align:middle line:90% from one day to the next day. 01:41:49.080 --> 01:41:52.940 align:middle line:84% It's kind of a very slow adjustment to reset their norms. 01:41:52.940 --> 01:41:56.240 align:middle line:84% So as such, if you wanted to go down that route, 01:41:56.240 --> 01:42:02.140 align:middle line:84% I wouldn't use the short time constants. 01:42:02.140 --> 01:42:05.200 align:middle line:84% But otherwise, the basic idea is fine. 01:42:05.200 --> 01:42:06.040 align:middle line:90% It works. 01:42:06.040 --> 01:42:11.720 align:middle line:84% I don't necessarily vouch for it as-- for this simple model. 01:42:11.720 --> 01:42:14.360 align:middle line:84% I think it's probably too much to capture, 01:42:14.360 --> 01:42:17.100 align:middle line:84% but it introduces some interesting dynamics. 01:42:17.100 --> 01:42:19.500 align:middle line:84% So you may want to try something like this 01:42:19.500 --> 01:42:21.500 align:middle line:90% for a theoretical model as well. 01:42:21.500 --> 01:42:24.980 align:middle line:84% Then the next step, he brings these together 01:42:24.980 --> 01:42:27.480 align:middle line:84% through an attended risk perception, 01:42:27.480 --> 01:42:29.900 align:middle line:84% which is basically a weighted average of these two, 01:42:29.900 --> 01:42:33.590 align:middle line:84% except that Gerardo is using two different weight 01:42:33.590 --> 01:42:35.810 align:middle line:84% parameters to create the weighing, 01:42:35.810 --> 01:42:39.310 align:middle line:84% and he basically is multiplying one with one weight 01:42:39.310 --> 01:42:42.790 align:middle line:84% and with the other weight, and dividing by the total weight. 01:42:42.790 --> 01:42:45.490 align:middle line:90% So good or bad? 01:42:45.490 --> 01:42:47.570 align:middle line:84% What's good, what's bad with this formulation? 01:42:47.570 --> 01:42:51.310 align:middle line:90% 01:42:51.310 --> 01:42:52.950 align:middle line:84% AUDIENCE: I think you can simplify it 01:42:52.950 --> 01:42:54.673 align:middle line:90% to just one parameter. 01:42:54.673 --> 01:42:55.590 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:42:55.590 --> 01:42:59.070 align:middle line:84% So basically, you can easily simplify and get 01:42:59.070 --> 01:43:01.650 align:middle line:84% the exact same behavior with a single parameter. 01:43:01.650 --> 01:43:03.470 align:middle line:90% So how would you do that, Alban? 01:43:03.470 --> 01:43:05.550 align:middle line:84% AUDIENCE: So it would be weight of death, 01:43:05.550 --> 01:43:08.272 align:middle line:90% and then you use 1 minus death. 01:43:08.272 --> 01:43:09.230 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:43:09.230 --> 01:43:11.030 align:middle line:84% So basically, you use weight of death 01:43:11.030 --> 01:43:12.910 align:middle line:90% and 1 minus weight of death. 01:43:12.910 --> 01:43:17.090 align:middle line:84% And with a single parameter, you get the exact same behavior, 01:43:17.090 --> 01:43:19.870 align:middle line:84% except that now you don't need two degrees of freedom 01:43:19.870 --> 01:43:22.270 align:middle line:84% and figuring out between two degrees of freedom 01:43:22.270 --> 01:43:24.510 align:middle line:84% how to parameterize that, and so on. 01:43:24.510 --> 01:43:27.270 align:middle line:84% Is that clear why they are equivalent? 01:43:27.270 --> 01:43:34.170 align:middle line:84% Basically, you divide this whole equation on the numerator by one 01:43:34.170 --> 01:43:36.210 align:middle line:84% of these things, weight of death, let's say. 01:43:36.210 --> 01:43:40.730 align:middle line:84% You will get to a single parameterized version of it 01:43:40.730 --> 01:43:43.270 align:middle line:90% without any loss of generality. 01:43:43.270 --> 01:43:45.382 align:middle line:84% OK, but conceptually, this is fine. 01:43:45.382 --> 01:43:46.590 align:middle line:90% There is nothing problematic. 01:43:46.590 --> 01:43:48.570 align:middle line:84% It's just that you can do it more efficiently. 01:43:48.570 --> 01:43:53.290 align:middle line:84% Then you get risk perception, simple formulation 01:43:53.290 --> 01:43:57.770 align:middle line:84% we are familiar with, except asymmetry is not captured here. 01:43:57.770 --> 01:44:00.810 align:middle line:90% But keep that in mind. 01:44:00.810 --> 01:44:04.850 align:middle line:84% And then you have the impact on use of safety measures 01:44:04.850 --> 01:44:08.310 align:middle line:90% versus impact on contact rate. 01:44:08.310 --> 01:44:13.090 align:middle line:84% So this risk perception is a simple-- 01:44:13.090 --> 01:44:14.470 align:middle line:90% a smooth function. 01:44:14.470 --> 01:44:17.690 align:middle line:84% So means the risk perceived, the risk perception 01:44:17.690 --> 01:44:21.790 align:middle line:84% in this function, what's the range of it? 01:44:21.790 --> 01:44:25.710 align:middle line:90% That is, how far up can it go? 01:44:25.710 --> 01:44:31.260 align:middle line:90% 01:44:31.260 --> 01:44:33.823 align:middle line:84% AUDIENCE: From 0 to something very high. 01:44:33.823 --> 01:44:34.740 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:44:34.740 --> 01:44:37.320 align:middle line:84% So it can go from 0 to something very high. 01:44:37.320 --> 01:44:41.100 align:middle line:84% But basically, it will not go below 0 01:44:41.100 --> 01:44:45.140 align:middle line:84% because the risk perception things here are fractions. 01:44:45.140 --> 01:44:48.860 align:middle line:84% And therefore, they would never go below 0. 01:44:48.860 --> 01:44:52.620 align:middle line:84% But it has no limits on the top side. 01:44:52.620 --> 01:44:53.920 align:middle line:90% Alexander, you have a question? 01:44:53.920 --> 01:44:56.060 align:middle line:84% AUDIENCE: Yeah Just going back to just the risk 01:44:56.060 --> 01:44:59.783 align:middle line:84% perception, Gerardo divides by the reference. 01:44:59.783 --> 01:45:00.700 align:middle line:90% HAZHIR RAHMANDAD: Yes. 01:45:00.700 --> 01:45:03.158 align:middle line:84% AUDIENCE: So if the reference is 0, which it could be like, 01:45:03.158 --> 01:45:05.900 align:middle line:84% there's no pandemic going on, how would you suggest-- 01:45:05.900 --> 01:45:06.140 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:45:06.140 --> 01:45:07.520 align:middle line:84% So that would be another problem. 01:45:07.520 --> 01:45:09.260 align:middle line:84% So basically, you would need some kind 01:45:09.260 --> 01:45:17.060 align:middle line:84% of a minimum reference of sorts to set that actual reference. 01:45:17.060 --> 01:45:19.420 align:middle line:84% That the indicated reference should also not 01:45:19.420 --> 01:45:21.800 align:middle line:84% go below the minimum reference or something. 01:45:21.800 --> 01:45:23.600 align:middle line:84% AUDIENCE: So is that realistic, though? 01:45:23.600 --> 01:45:25.500 align:middle line:84% Because let's say like before COVID, 01:45:25.500 --> 01:45:27.760 align:middle line:84% people's reference for COVID deaths 01:45:27.760 --> 01:45:29.842 align:middle line:90% was 0 because it didn't exist. 01:45:29.842 --> 01:45:30.800 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:45:30.800 --> 01:45:36.500 align:middle line:84% So it is not-- you shouldn't think of it as reference-- 01:45:36.500 --> 01:45:38.800 align:middle line:84% so you should define what is reference for yourself 01:45:38.800 --> 01:45:39.820 align:middle line:90% very clearly. 01:45:39.820 --> 01:45:42.160 align:middle line:84% So we should define reference in this case 01:45:42.160 --> 01:45:46.080 align:middle line:84% as the level of COVID case, or the level of disease 01:45:46.080 --> 01:45:50.720 align:middle line:84% that basically triggers people's attention. 01:45:50.720 --> 01:45:54.980 align:middle line:84% So if you define it that way, that triggering level is not 0. 01:45:54.980 --> 01:45:58.140 align:middle line:84% It's something positive, but not a large number. 01:45:58.140 --> 01:46:00.360 align:middle line:84% And it would never go completely to 0 01:46:00.360 --> 01:46:04.300 align:middle line:84% because there are all sources of death and misery around us. 01:46:04.300 --> 01:46:09.727 align:middle line:84% So if there is one deaths per million per year for some topic, 01:46:09.727 --> 01:46:11.060 align:middle line:90% we probably don't care about it. 01:46:11.060 --> 01:46:12.018 align:middle line:90% We don't hear about it. 01:46:12.018 --> 01:46:15.320 align:middle line:84% It doesn't come to our attention space. 01:46:15.320 --> 01:46:19.840 align:middle line:84% So therefore, the risk perception-- now going back 01:46:19.840 --> 01:46:24.650 align:middle line:84% to the conversation-- is between 0 and a large number. 01:46:24.650 --> 01:46:30.330 align:middle line:84% So how does that impact current contact rate? 01:46:30.330 --> 01:46:34.310 align:middle line:90% So this part is not clear to me. 01:46:34.310 --> 01:46:36.930 align:middle line:90% 01:46:36.930 --> 01:46:39.250 align:middle line:84% AUDIENCE: Here, I start to struggle 01:46:39.250 --> 01:46:42.410 align:middle line:84% to try to make sense with this formulation. 01:46:42.410 --> 01:46:46.050 align:middle line:84% But I think that on contact rate, I have some trouble-- 01:46:46.050 --> 01:46:49.350 align:middle line:84% or some problem, probably on the other part, 01:46:49.350 --> 01:46:53.252 align:middle line:84% like the detection is a little bit-- 01:46:53.252 --> 01:46:54.210 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:46:54.210 --> 01:46:56.450 align:middle line:84% So let's look at this formulation, not 01:46:56.450 --> 01:46:59.050 align:middle line:84% to try to correct it, but just to highlight 01:46:59.050 --> 01:47:01.750 align:middle line:90% a few general observations. 01:47:01.750 --> 01:47:04.570 align:middle line:90% So this formulation is messy. 01:47:04.570 --> 01:47:08.010 align:middle line:84% Kind of, I look at it, and I say, OK I can't follow. 01:47:08.010 --> 01:47:12.670 align:middle line:84% And because it has a few operations happening into it, 01:47:12.670 --> 01:47:18.050 align:middle line:84% you have some subtractions, some multiplication 01:47:18.050 --> 01:47:19.270 align:middle line:90% of three different things. 01:47:19.270 --> 01:47:21.070 align:middle line:84% You have this extra parentheses that 01:47:21.070 --> 01:47:23.870 align:middle line:84% is just syntax that confuses, but it still 01:47:23.870 --> 01:47:25.630 align:middle line:90% makes it even harder. 01:47:25.630 --> 01:47:28.410 align:middle line:84% And so I can't really make sense of it. 01:47:28.410 --> 01:47:32.030 align:middle line:84% It just would suggest that the logic behind it 01:47:32.030 --> 01:47:35.010 align:middle line:84% is not very well thought through. 01:47:35.010 --> 01:47:36.850 align:middle line:84% You don't have a very clean logic. 01:47:36.850 --> 01:47:38.950 align:middle line:84% It makes it very hard for yourself and for others 01:47:38.950 --> 01:47:39.770 align:middle line:90% to understand it. 01:47:39.770 --> 01:47:45.310 align:middle line:84% So this is kind of an example of try to make the logic that you 01:47:45.310 --> 01:47:48.710 align:middle line:84% are trying to follow very clear, operational, 01:47:48.710 --> 01:47:50.150 align:middle line:90% then write the equation. 01:47:50.150 --> 01:47:55.510 align:middle line:84% Now, the other thing is that basically this formulation 01:47:55.510 --> 01:47:58.310 align:middle line:84% is not robust because the current contact rate that 01:47:58.310 --> 01:48:02.932 align:middle line:84% will come out of it is likely to go outside of the range 01:48:02.932 --> 01:48:03.890 align:middle line:90% that you want it to be. 01:48:03.890 --> 01:48:05.598 align:middle line:84% So the current contact rate should always 01:48:05.598 --> 01:48:09.430 align:middle line:84% be between 0 and the maximum contact 01:48:09.430 --> 01:48:12.670 align:middle line:84% your, normal contact rate absent cases and deaths. 01:48:12.670 --> 01:48:17.030 align:middle line:84% So enforcing that constraint within this formulation 01:48:17.030 --> 01:48:20.370 align:middle line:84% is, I think, what Gerardo was trying to do. 01:48:20.370 --> 01:48:23.510 align:middle line:84% And that's how he got into this more complex formulation. 01:48:23.510 --> 01:48:25.730 align:middle line:84% He was testing it and not getting the result 01:48:25.730 --> 01:48:28.930 align:middle line:84% that he wanted, and coming up with other formulations 01:48:28.930 --> 01:48:31.390 align:middle line:90% to fix the problem. 01:48:31.390 --> 01:48:34.590 align:middle line:84% But it started with a wrong foundation. 01:48:34.590 --> 01:48:37.370 align:middle line:84% It just-- you can't get to the right thing. 01:48:37.370 --> 01:48:39.350 align:middle line:84% You actually don't need a stock for sure, 01:48:39.350 --> 01:48:42.570 align:middle line:84% because you already have the delays in the risk perception 01:48:42.570 --> 01:48:43.870 align:middle line:90% process captured. 01:48:43.870 --> 01:48:45.650 align:middle line:84% So adding a stock is already kind 01:48:45.650 --> 01:48:48.410 align:middle line:84% of creating lots of confusion, because now you 01:48:48.410 --> 01:48:51.550 align:middle line:84% have to worry about the stock and flow relationships. 01:48:51.550 --> 01:48:55.770 align:middle line:84% It's a mess to figure that problem. 01:48:55.770 --> 01:48:58.610 align:middle line:84% So I think that was a good example 01:48:58.610 --> 01:49:04.210 align:middle line:84% to critique a few other-- or identify a few other challenges. 01:49:04.210 --> 01:49:05.930 align:middle line:90% Any other volunteers? 01:49:05.930 --> 01:49:07.510 align:middle line:90% I volunteered you. 01:49:07.510 --> 01:49:09.642 align:middle line:90% AUDIENCE: Can we see Alban's? 01:49:09.642 --> 01:49:11.850 align:middle line:84% HAZHIR RAHMANDAD: Alban, do you want us to see yours? 01:49:11.850 --> 01:49:12.330 align:middle line:90% AUDIENCE: Sure. 01:49:12.330 --> 01:49:13.205 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:49:13.205 --> 01:49:15.490 align:middle line:90% 01:49:15.490 --> 01:49:16.590 align:middle line:90% Good layout. 01:49:16.590 --> 01:49:19.980 align:middle line:90% 01:49:19.980 --> 01:49:21.120 align:middle line:90% One unit error. 01:49:21.120 --> 01:49:25.220 align:middle line:90% 01:49:25.220 --> 01:49:28.380 align:middle line:84% AUDIENCE: I didn't normalize the perseverance 01:49:28.380 --> 01:49:30.020 align:middle line:90% to the impact of the-- 01:49:30.020 --> 01:49:31.060 align:middle line:90% HAZHIR RAHMANDAD: I see. 01:49:31.060 --> 01:49:31.900 align:middle line:90% OK. 01:49:31.900 --> 01:49:36.260 align:middle line:84% So you are getting the indicated risk from death rate. 01:49:36.260 --> 01:49:37.540 align:middle line:90% That's OK. 01:49:37.540 --> 01:49:43.020 align:middle line:84% As we discussed, we could get it from the-- 01:49:43.020 --> 01:49:46.240 align:middle line:84% we could get it from the infection as well, 01:49:46.240 --> 01:49:47.880 align:middle line:84% but I'm fine with just using death. 01:49:47.880 --> 01:49:50.460 align:middle line:84% Death is probably a stronger driver 01:49:50.460 --> 01:49:53.820 align:middle line:84% of risk perception in most communities. 01:49:53.820 --> 01:49:57.160 align:middle line:84% And then indicated risk becomes perceived risk. 01:49:57.160 --> 01:50:01.460 align:middle line:84% You can see that the asymmetric risk adjustment is approached, 01:50:01.460 --> 01:50:03.900 align:middle line:90% is applied here, which is good. 01:50:03.900 --> 01:50:08.860 align:middle line:84% And then the impact uses a sensitivity parameter which 01:50:08.860 --> 01:50:12.200 align:middle line:90% is similar to what Jason had. 01:50:12.200 --> 01:50:15.740 align:middle line:84% So this is very similar to the formulation Jason had. 01:50:15.740 --> 01:50:16.420 align:middle line:90% It works fine. 01:50:16.420 --> 01:50:18.480 align:middle line:84% It's a good first-order approximation. 01:50:18.480 --> 01:50:21.400 align:middle line:84% We could come up with alternatives. 01:50:21.400 --> 01:50:26.560 align:middle line:90% We can actually think about-- 01:50:26.560 --> 01:50:34.120 align:middle line:84% so a simple alternative would be 1 over 1 01:50:34.120 --> 01:50:41.120 align:middle line:84% plus perceived risk multiplied by a factor, a kind of a scaling 01:50:41.120 --> 01:50:42.080 align:middle line:90% factor. 01:50:42.080 --> 01:50:47.080 align:middle line:84% So that also will be remaining between 0 and 1. 01:50:47.080 --> 01:50:50.600 align:middle line:84% That is, if the perceived risk is high, 01:50:50.600 --> 01:50:54.440 align:middle line:84% or the multiplying factor, that that factor is high. 01:50:54.440 --> 01:50:56.460 align:middle line:90% It will go towards 0. 01:50:56.460 --> 01:50:58.685 align:middle line:84% But it would go towards zero much more slowly. 01:50:58.685 --> 01:51:00.560 align:middle line:84% So when we are dealing with these things that 01:51:00.560 --> 01:51:03.160 align:middle line:84% may change orders of magnitude, that 01:51:03.160 --> 01:51:07.600 align:middle line:84% is an easier, simpler formulation to work with. 01:51:07.600 --> 01:51:10.040 align:middle line:84% You could also add another parameter 01:51:10.040 --> 01:51:12.930 align:middle line:84% that controls the strength of this slope 01:51:12.930 --> 01:51:18.130 align:middle line:84% by, for example, 1 over 1 plus perceived risk 01:51:18.130 --> 01:51:21.410 align:middle line:84% to the power of some alpha multiplied 01:51:21.410 --> 01:51:23.470 align:middle line:90% by that factor, whatever it was. 01:51:23.470 --> 01:51:29.530 align:middle line:84% And that alpha can control how responsive you are to risk. 01:51:29.530 --> 01:51:31.150 align:middle line:90% But this is fine. 01:51:31.150 --> 01:51:35.810 align:middle line:84% Those are a couple of simple alternatives you could use. 01:51:35.810 --> 01:51:39.050 align:middle line:84% Let's now go to the vaccination part. 01:51:39.050 --> 01:51:42.290 align:middle line:84% So we have the vaccination process 01:51:42.290 --> 01:51:44.430 align:middle line:84% with vaccination-- fractional vaccination. 01:51:44.430 --> 01:51:53.170 align:middle line:84% So it is kind of missing the formulation for people not being 01:51:53.170 --> 01:51:54.590 align:middle line:90% interested in vaccination. 01:51:54.590 --> 01:51:58.030 align:middle line:84% So it is assuming that everybody is interested in vaccination. 01:51:58.030 --> 01:52:00.650 align:middle line:90% 01:52:00.650 --> 01:52:04.050 align:middle line:84% And then the vaccinated population, I'm assuming 01:52:04.050 --> 01:52:07.290 align:middle line:84% is going through the same process. 01:52:07.290 --> 01:52:14.010 align:middle line:84% You have the unvaccinated also impacting the infection rate. 01:52:14.010 --> 01:52:15.870 align:middle line:84% So you have the unvaccinated plus vaccinated 01:52:15.870 --> 01:52:17.850 align:middle line:90% divided by total population. 01:52:17.850 --> 01:52:21.970 align:middle line:84% So remember the assumption that comes with this formulation. 01:52:21.970 --> 01:52:26.390 align:middle line:84% The assumption is here that unvaccinated and vaccinated 01:52:26.390 --> 01:52:29.470 align:middle line:84% have the same level of infectivity. 01:52:29.470 --> 01:52:33.570 align:middle line:84% So that assumption is built into this formulation, 01:52:33.570 --> 01:52:38.910 align:middle line:84% but it's easy to relax that by adding that factor that we 01:52:38.910 --> 01:52:44.190 align:middle line:90% saw in Russ's formulation. 01:52:44.190 --> 01:52:50.010 align:middle line:84% And then-- let's see, what else here matters? 01:52:50.010 --> 01:52:57.950 align:middle line:84% So an interesting part of it is loss of vaccination, 01:52:57.950 --> 01:52:59.490 align:middle line:90% waning of vaccination. 01:52:59.490 --> 01:53:08.960 align:middle line:90% 01:53:08.960 --> 01:53:09.460 align:middle line:90% Yeah. 01:53:09.460 --> 01:53:17.400 align:middle line:84% So the immunity period takes people out into unvaccinated. 01:53:17.400 --> 01:53:19.060 align:middle line:90% And then the duration of-- 01:53:19.060 --> 01:53:21.960 align:middle line:90% 01:53:21.960 --> 01:53:22.500 align:middle line:90% oh, OK. 01:53:22.500 --> 01:53:27.799 align:middle line:84% So here, we don't have vaccinated recovered, correct? 01:53:27.799 --> 01:53:28.466 align:middle line:90% AUDIENCE: Right. 01:53:28.466 --> 01:53:32.165 align:middle line:84% HAZHIR RAHMANDAD: And that is a little bit of a judgment call. 01:53:32.165 --> 01:53:33.040 align:middle line:90% So this is actually-- 01:53:33.040 --> 01:53:36.480 align:middle line:84% I think Hesam had the same assumption, that when 01:53:36.480 --> 01:53:46.400 align:middle line:84% people get sick and they recover, 01:53:46.400 --> 01:53:49.800 align:middle line:84% should we keep them separate into a stock and flow 01:53:49.800 --> 01:53:53.320 align:middle line:84% chain of vaccinated, but recovered, 01:53:53.320 --> 01:53:58.360 align:middle line:84% or just dump them into the group of unvaccinated recovered 01:53:58.360 --> 01:54:01.400 align:middle line:90% or total recovered? 01:54:01.400 --> 01:54:06.900 align:middle line:84% So that distinction may matter in two settings. 01:54:06.900 --> 01:54:10.300 align:middle line:84% One is for our vaccination rate, because 01:54:10.300 --> 01:54:12.940 align:middle line:84% for being able to decide how many people we need 01:54:12.940 --> 01:54:16.100 align:middle line:84% to vaccinate, we need to know how many people are vaccinated 01:54:16.100 --> 01:54:18.260 align:middle line:84% and recovered, but not interested in vaccination 01:54:18.260 --> 01:54:21.220 align:middle line:84% right now because they have recently been vaccinated. 01:54:21.220 --> 01:54:24.300 align:middle line:84% So that part would not be able-- we would not 01:54:24.300 --> 01:54:25.820 align:middle line:84% be able to separate if we don't have 01:54:25.820 --> 01:54:27.900 align:middle line:84% the stock of recovered vaccinated 01:54:27.900 --> 01:54:32.940 align:middle line:90% versus unvaccinated recovered. 01:54:32.940 --> 01:54:34.900 align:middle line:84% The second part that it may matter 01:54:34.900 --> 01:54:37.700 align:middle line:90% is about differences in delays. 01:54:37.700 --> 01:54:44.660 align:middle line:84% So if my vaccine immunity lasts for a longer time 01:54:44.660 --> 01:54:48.880 align:middle line:84% than my natural immunity-- so let's, for extreme conditions, 01:54:48.880 --> 01:54:51.220 align:middle line:84% say natural immunity lasts for a month. 01:54:51.220 --> 01:54:54.220 align:middle line:84% Vaccine immunity lasts for a year. 01:54:54.220 --> 01:54:57.180 align:middle line:84% Now, if I don't separate these two groups, 01:54:57.180 --> 01:55:01.300 align:middle line:84% once somebody vaccinated gets sick, 01:55:01.300 --> 01:55:06.790 align:middle line:84% we are dumping them into the group that will quickly 01:55:06.790 --> 01:55:11.670 align:middle line:84% lose their immunity because they got the disease, 01:55:11.670 --> 01:55:16.570 align:middle line:84% and through the natural basically loss of immunity, 01:55:16.570 --> 01:55:19.910 align:middle line:84% they will become susceptible very quickly. 01:55:19.910 --> 01:55:23.670 align:middle line:84% So I have basically nullified the value of vaccine 01:55:23.670 --> 01:55:26.910 align:middle line:84% that would otherwise last for a year for these folks. 01:55:26.910 --> 01:55:33.230 align:middle line:84% So that's the second reason why this separation does make sense. 01:55:33.230 --> 01:55:35.690 align:middle line:84% Now, there is another interesting point here. 01:55:35.690 --> 01:55:37.130 align:middle line:90% That is, what about the reverse? 01:55:37.130 --> 01:55:43.070 align:middle line:84% That is, if we had the case that people who get vaccinated 01:55:43.070 --> 01:55:47.990 align:middle line:84% have much shorter waning time than people 01:55:47.990 --> 01:55:49.290 align:middle line:90% who get natural immunity. 01:55:49.290 --> 01:55:52.890 align:middle line:84% So it takes a year after getting the disease to recover. 01:55:52.890 --> 01:55:55.790 align:middle line:84% But after a month of vaccine, you 01:55:55.790 --> 01:55:57.950 align:middle line:90% are going to lose your immunity. 01:55:57.950 --> 01:55:59.910 align:middle line:90% What should we do. 01:55:59.910 --> 01:56:10.170 align:middle line:84% So in that case, having this stock of vaccinated recovered, 01:56:10.170 --> 01:56:13.850 align:middle line:90% you would let them wane-- 01:56:13.850 --> 01:56:16.550 align:middle line:84% by waning of their immunity from vaccine, 01:56:16.550 --> 01:56:19.210 align:middle line:84% they would go into the recovered population 01:56:19.210 --> 01:56:22.050 align:middle line:90% without vaccine immunity. 01:56:22.050 --> 01:56:25.170 align:middle line:84% And then they would lose longer-term immunity 01:56:25.170 --> 01:56:30.770 align:middle line:84% from natural vaccination, some natural disease, 01:56:30.770 --> 01:56:33.470 align:middle line:84% and go back into the susceptible population. 01:56:33.470 --> 01:56:35.910 align:middle line:84% So that way, you get their double protection. 01:56:35.910 --> 01:56:38.970 align:middle line:84% You don't lose that double protection. 01:56:38.970 --> 01:56:42.850 align:middle line:90% Is this conversation clear? 01:56:42.850 --> 01:56:44.533 align:middle line:84% Jake, you had a question or that-- 01:56:44.533 --> 01:56:45.950 align:middle line:84% AUDIENCE: You've kind of answered? 01:56:45.950 --> 01:56:48.610 align:middle line:90% HAZHIR RAHMANDAD: OK. 01:56:48.610 --> 01:56:50.690 align:middle line:90% Alexander? 01:56:50.690 --> 01:56:52.890 align:middle line:84% AUDIENCE: So in that structure, people 01:56:52.890 --> 01:56:56.170 align:middle line:84% go from vaccinated infected to vaccinated recovered. 01:56:56.170 --> 01:56:59.850 align:middle line:84% And then because vaccination immunity is so little, 01:56:59.850 --> 01:57:02.420 align:middle line:90% you go into recovery population. 01:57:02.420 --> 01:57:06.300 align:middle line:84% And then so that's what happens if waning for vaccination 01:57:06.300 --> 01:57:08.920 align:middle line:84% happens much shorter than natural. 01:57:08.920 --> 01:57:10.300 align:middle line:90% So then what if there-- 01:57:10.300 --> 01:57:11.940 align:middle line:84% maybe you already said this, and I-- 01:57:11.940 --> 01:57:15.020 align:middle line:84% like if the reverse is true, if the natural immunity 01:57:15.020 --> 01:57:17.260 align:middle line:84% is much shorter than vaccination period, 01:57:17.260 --> 01:57:19.700 align:middle line:84% does that mean that you go from vaccinated-- 01:57:19.700 --> 01:57:22.260 align:middle line:84% HAZHIR RAHMANDAD: It is OK to then still drain them 01:57:22.260 --> 01:57:27.940 align:middle line:84% into recovered but unvaccinated because then they will quickly 01:57:27.940 --> 01:57:32.500 align:middle line:90% go into the susceptible part. 01:57:32.500 --> 01:57:36.780 align:middle line:84% It is OK to do that, but it is not necessarily the best way 01:57:36.780 --> 01:57:37.520 align:middle line:90% to do it. 01:57:37.520 --> 01:57:43.060 align:middle line:84% You could also go straight to susceptible unvaccinated 01:57:43.060 --> 01:57:46.048 align:middle line:90% because you-- 01:57:46.048 --> 01:57:47.340 align:middle line:90% AUDIENCE: Vaccinated recovered. 01:57:47.340 --> 01:57:49.090 align:middle line:84% HAZHIR RAHMANDAD: Yes, because you got out 01:57:49.090 --> 01:57:51.640 align:middle line:90% of the vaccine-- yes. 01:57:51.640 --> 01:57:54.520 align:middle line:84% You lost your immunity after a long time. 01:57:54.520 --> 01:57:56.580 align:middle line:84% So you have by default already lost 01:57:56.580 --> 01:58:01.360 align:middle line:84% your immunity because of the natural immunity. 01:58:01.360 --> 01:58:05.480 align:middle line:84% So in a sense, this is an interesting situation 01:58:05.480 --> 01:58:09.240 align:middle line:84% where the value of the parameter could potentially 01:58:09.240 --> 01:58:12.720 align:middle line:84% change the structure you use for the flows. 01:58:12.720 --> 01:58:18.080 align:middle line:84% That is, if the natural immunity is much longer than the vaccine 01:58:18.080 --> 01:58:25.520 align:middle line:84% immunity, you definitely want to drain the vaccinated recovered 01:58:25.520 --> 01:58:31.120 align:middle line:84% into the naturally recovered and let them stay there for as long 01:58:31.120 --> 01:58:34.080 align:middle line:84% as the natural immunity helps them with. 01:58:34.080 --> 01:58:39.960 align:middle line:84% But in the reverse case, if natural immunity is shorter 01:58:39.960 --> 01:58:45.120 align:middle line:84% than the vaccine immunity, it may be actually more objectively 01:58:45.120 --> 01:58:50.160 align:middle line:84% correct to go from vaccine recovered all 01:58:50.160 --> 01:58:55.160 align:middle line:84% the way to susceptible unvaccinated, 01:58:55.160 --> 01:58:59.620 align:middle line:84% because by the fact that you have finished your vaccine 01:58:59.620 --> 01:59:05.660 align:middle line:84% immunity, by definition, you will lose your natural immunity 01:59:05.660 --> 01:59:06.480 align:middle line:90% as well. 01:59:06.480 --> 01:59:09.700 align:middle line:84% AUDIENCE: So couldn't you do that in the other case 01:59:09.700 --> 01:59:13.060 align:middle line:84% as well, that you just have a separate immunity waning 01:59:13.060 --> 01:59:16.260 align:middle line:84% time constant for people who are vaccinated and recovered? 01:59:16.260 --> 01:59:20.100 align:middle line:84% And you just make that longer than that of people who 01:59:20.100 --> 01:59:22.020 align:middle line:90% are unvaccinated but recovered? 01:59:22.020 --> 01:59:23.820 align:middle line:84% And it's longer because it's not-- 01:59:23.820 --> 01:59:25.163 align:middle line:90% I guess I don't [INAUDIBLE]. 01:59:25.163 --> 01:59:27.080 align:middle line:84% HAZHIR RAHMANDAD: So it's not exactly the sum. 01:59:27.080 --> 01:59:28.895 align:middle line:90% Yeah, you could do that as well. 01:59:28.895 --> 01:59:30.020 align:middle line:90% AUDIENCE: But that's like-- 01:59:30.020 --> 01:59:33.660 align:middle line:84% it's the same as going from vaccinated recovered 01:59:33.660 --> 01:59:35.620 align:middle line:90% to unvaccinated recovered. 01:59:35.620 --> 01:59:38.540 align:middle line:84% So it would just be first-order instead of two. 01:59:38.540 --> 01:59:42.382 align:middle line:84% But it's still just sum of the time constants. 01:59:42.382 --> 01:59:43.340 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 01:59:43.340 --> 01:59:44.960 align:middle line:90% Not exactly the sum, but yes. 01:59:44.960 --> 01:59:47.660 align:middle line:90% 01:59:47.660 --> 01:59:52.140 align:middle line:84% So yeah, I think you could do that as well. 01:59:52.140 --> 01:59:54.260 align:middle line:90% Cathy? 01:59:54.260 --> 01:59:58.370 align:middle line:84% AUDIENCE: I think I'm still a little confused in my mind. 01:59:58.370 --> 02:00:02.010 align:middle line:84% I think if a vaccinated person is infected, 02:00:02.010 --> 02:00:04.310 align:middle line:90% then their immunity wanes. 02:00:04.310 --> 02:00:07.190 align:middle line:84% They didn't have immunity, too, and so they 02:00:07.190 --> 02:00:09.030 align:middle line:90% might have a better outcome. 02:00:09.030 --> 02:00:12.590 align:middle line:90% But do we need to consider-- 02:00:12.590 --> 02:00:15.490 align:middle line:84% like so the vaccinated person gets sick, 02:00:15.490 --> 02:00:17.430 align:middle line:84% but then once they recover, they still 02:00:17.430 --> 02:00:20.090 align:middle line:90% have some vaccination immunity. 02:00:20.090 --> 02:00:22.310 align:middle line:90% To me, that doesn't equate. 02:00:22.310 --> 02:00:24.470 align:middle line:84% HAZHIR RAHMANDAD: So it is actually 02:00:24.470 --> 02:00:27.550 align:middle line:84% kind of a very objective biological question 02:00:27.550 --> 02:00:29.968 align:middle line:84% that I don't have a good answer for it. 02:00:29.968 --> 02:00:31.510 align:middle line:84% And I don't think even the literature 02:00:31.510 --> 02:00:32.552 align:middle line:90% has a good answer for it. 02:00:32.552 --> 02:00:34.150 align:middle line:84% This is kind of one of those areas 02:00:34.150 --> 02:00:36.710 align:middle line:84% that I've seen enough models to know that people don't 02:00:36.710 --> 02:00:39.110 align:middle line:90% know what exactly is happening. 02:00:39.110 --> 02:00:40.930 align:middle line:84% So depending on the story you tell, 02:00:40.930 --> 02:00:43.890 align:middle line:84% you could actually build the model a little bit differently. 02:00:43.890 --> 02:00:47.390 align:middle line:84% So one story is that the fact that you got the disease 02:00:47.390 --> 02:00:49.810 align:middle line:84% is a signal that you didn't have the immunity-- 02:00:49.810 --> 02:00:51.685 align:middle line:90% much immunity from the vaccine. 02:00:51.685 --> 02:00:53.310 align:middle line:84% And therefore, by the time you recover, 02:00:53.310 --> 02:00:56.050 align:middle line:84% you should just go like the people who don't 02:00:56.050 --> 02:00:57.430 align:middle line:90% have any immunity from vaccine. 02:00:57.430 --> 02:01:00.890 align:middle line:84% There is no residual vaccine immunity left for you. 02:01:00.890 --> 02:01:04.490 align:middle line:84% The other story is that no, it's a stochastic process. 02:01:04.490 --> 02:01:09.030 align:middle line:84% And if you get unlucky or enough exposure, 02:01:09.030 --> 02:01:13.710 align:middle line:84% and so on, it may penetrate your defenses through vaccine. 02:01:13.710 --> 02:01:17.290 align:middle line:84% But it doesn't mean those defenses don't exist. 02:01:17.290 --> 02:01:21.610 align:middle line:84% And therefore, those defenses may still last actually 02:01:21.610 --> 02:01:23.630 align:middle line:84% for a while after your natural immunity, 02:01:23.630 --> 02:01:25.490 align:middle line:84% and it's worth keeping track of those. 02:01:25.490 --> 02:01:30.170 align:middle line:84% Those two different stories, probably both of them 02:01:30.170 --> 02:01:31.113 align:middle line:90% are operating. 02:01:31.113 --> 02:01:33.530 align:middle line:84% The thing is that we do have heterogeneity, and some of it 02:01:33.530 --> 02:01:34.988 align:middle line:84% is that people who are getting sick 02:01:34.988 --> 02:01:37.730 align:middle line:84% are the ones who don't have as much-- 02:01:37.730 --> 02:01:39.710 align:middle line:84% don't benefit as much from the vaccines. 02:01:39.710 --> 02:01:42.150 align:middle line:84% But also there is the stochastic nature of it. 02:01:42.150 --> 02:01:46.050 align:middle line:84% So yeah, we're going more with the stochastic story 02:01:46.050 --> 02:01:48.590 align:middle line:84% than with the complete heterogeneity. 02:01:48.590 --> 02:01:51.260 align:middle line:84% In fact, if you wanted to capture that heterogeneity 02:01:51.260 --> 02:01:54.740 align:middle line:84% really robustly, the better way to do it 02:01:54.740 --> 02:01:57.100 align:middle line:84% would be to separate the population, those 02:01:57.100 --> 02:02:01.020 align:middle line:84% who are benefiting from vaccine versus those who are not 02:02:01.020 --> 02:02:02.700 align:middle line:84% benefiting that much from vaccine 02:02:02.700 --> 02:02:05.880 align:middle line:84% because their immune system is not compatible or whatever. 02:02:05.880 --> 02:02:08.820 align:middle line:84% They don't get enough a response and so on. 02:02:08.820 --> 02:02:12.597 align:middle line:84% AUDIENCE: I'm curious to know how formulated would be at risk. 02:02:12.597 --> 02:02:14.180 align:middle line:84% HAZHIR RAHMANDAD: So I think it should 02:02:14.180 --> 02:02:15.832 align:middle line:90% be pretty much the same as-- 02:02:15.832 --> 02:02:17.540 align:middle line:84% AUDIENCE: It looks like it's just the sum 02:02:17.540 --> 02:02:20.640 align:middle line:84% HAZHIR RAHMANDAD: It's just indicated risk. 02:02:20.640 --> 02:02:24.800 align:middle line:90% It's just-- yes, the sum. 02:02:24.800 --> 02:02:26.900 align:middle line:90% Yes. 02:02:26.900 --> 02:02:29.603 align:middle line:84% AUDIENCE: So this is the simplest possible way to-- 02:02:29.603 --> 02:02:31.020 align:middle line:84% HAZHIR RAHMANDAD: Yeah, this would 02:02:31.020 --> 02:02:32.540 align:middle line:90% be the simplest possible way. 02:02:32.540 --> 02:02:34.000 align:middle line:84% It's a pretty decent formulation. 02:02:34.000 --> 02:02:37.152 align:middle line:84% So actually, for most of our simple models of COVID, 02:02:37.152 --> 02:02:38.360 align:middle line:90% this is actually what we use. 02:02:38.360 --> 02:02:42.020 align:middle line:84% We didn't even work through the infection rate 02:02:42.020 --> 02:02:43.720 align:middle line:90% as a source of risk. 02:02:43.720 --> 02:02:47.180 align:middle line:84% We just use death rate, because then it 02:02:47.180 --> 02:02:49.240 align:middle line:84% kind of captures very well the fact 02:02:49.240 --> 02:02:52.860 align:middle line:84% that over time, as the risk of death goes down, 02:02:52.860 --> 02:02:54.760 align:middle line:84% people become much more comfortable 02:02:54.760 --> 02:02:57.280 align:middle line:90% and are not as concerned. 02:02:57.280 --> 02:02:59.480 align:middle line:84% These days, people don't talk about COVID. 02:02:59.480 --> 02:03:02.240 align:middle line:84% COVID is happening around us quite a bit. 02:03:02.240 --> 02:03:05.820 align:middle line:84% In fact, the infection rates are similar to 2022. 02:03:05.820 --> 02:03:07.720 align:middle line:90% It's not that different. 02:03:07.720 --> 02:03:10.400 align:middle line:84% We don't have the Omicron peak, but other than that, 02:03:10.400 --> 02:03:13.660 align:middle line:84% you look at the wastewater data from Boston, 02:03:13.660 --> 02:03:15.720 align:middle line:84% you see that we are dealing with COVID rates that 02:03:15.720 --> 02:03:19.780 align:middle line:84% are very similar to the normal pandemic year-- not normal, 02:03:19.780 --> 02:03:21.440 align:middle line:90% very unnormal pandemic year. 02:03:21.440 --> 02:03:23.160 align:middle line:84% But people are not dying as much, 02:03:23.160 --> 02:03:24.460 align:middle line:90% even though people are dying. 02:03:24.460 --> 02:03:26.900 align:middle line:84% So I don't know what's the number today, 02:03:26.900 --> 02:03:29.800 align:middle line:84% but it's in the order of I think 60,000 people per year 02:03:29.800 --> 02:03:30.420 align:middle line:90% in the US. 02:03:30.420 --> 02:03:32.460 align:middle line:90% So it's not trivial at all. 02:03:32.460 --> 02:03:35.620 align:middle line:84% But don't quote me on that number. 02:03:35.620 --> 02:03:37.680 align:middle line:84% It's just kind of a guesstimate for where we are. 02:03:37.680 --> 02:03:42.462 align:middle line:90% So I think we-- 02:03:42.462 --> 02:03:43.920 align:middle line:84% AUDIENCE: I have a general question 02:03:43.920 --> 02:03:44.880 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:03:44.880 --> 02:03:48.530 align:middle line:84% AUDIENCE: So from here, we obviously 02:03:48.530 --> 02:03:52.450 align:middle line:84% have a lot of parameters and different weights. 02:03:52.450 --> 02:03:55.450 align:middle line:84% How are we thinking about moving forward 02:03:55.450 --> 02:03:57.168 align:middle line:84% in terms of actually tuning all of those? 02:03:57.168 --> 02:03:58.710 align:middle line:84% HAZHIR RAHMANDAD: Very good question. 02:03:58.710 --> 02:03:58.970 align:middle line:90% AUDIENCE: [INAUDIBLE] 02:03:58.970 --> 02:03:59.928 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 02:03:59.928 --> 02:04:01.610 align:middle line:84% So first of all, how many parameters 02:04:01.610 --> 02:04:04.770 align:middle line:90% do we really need in this model? 02:04:04.770 --> 02:04:06.390 align:middle line:84% OK, let's go through this-- actually, 02:04:06.390 --> 02:04:08.630 align:middle line:84% Alban's model is a good exercise for that. 02:04:08.630 --> 02:04:11.210 align:middle line:84% And I think this is a good exercise in general. 02:04:11.210 --> 02:04:16.050 align:middle line:84% So we need two parameters here for the risk perception 02:04:16.050 --> 02:04:18.610 align:middle line:90% adjustment. 02:04:18.610 --> 02:04:22.850 align:middle line:84% We need one parameter for infection fatality rate 02:04:22.850 --> 02:04:27.970 align:middle line:84% and one parameter for impact of vaccination on fatality rate. 02:04:27.970 --> 02:04:29.930 align:middle line:90% Those are mandatory. 02:04:29.930 --> 02:04:34.170 align:middle line:84% We need something for the contact rate 02:04:34.170 --> 02:04:36.510 align:middle line:84% and infectivity multiplied with each other. 02:04:36.510 --> 02:04:39.310 align:middle line:84% So we don't need both of them, really. 02:04:39.310 --> 02:04:42.490 align:middle line:84% But in the SIR model, in business dynamics, 02:04:42.490 --> 02:04:45.390 align:middle line:84% we use those for clarity of the logic, 02:04:45.390 --> 02:04:48.970 align:middle line:84% because they are completely overlapping with each other. 02:04:48.970 --> 02:04:50.950 align:middle line:90% So there is one parameter there. 02:04:50.950 --> 02:04:54.910 align:middle line:84% There is one sensitivity parameter here. 02:04:54.910 --> 02:04:58.610 align:middle line:84% There is the recovery time and waning period. 02:04:58.610 --> 02:05:01.710 align:middle line:84% So you would have two waning periods for vaccination 02:05:01.710 --> 02:05:05.230 align:middle line:90% and for the normal. 02:05:05.230 --> 02:05:08.670 align:middle line:84% And then you have something about fraction of population 02:05:08.670 --> 02:05:11.430 align:middle line:90% that is open to vaccination. 02:05:11.430 --> 02:05:15.790 align:middle line:84% So that's about a dozen parameters total. 02:05:15.790 --> 02:05:19.450 align:middle line:84% Would this model be identifiable-- so first of all, 02:05:19.450 --> 02:05:24.130 align:middle line:84% if you make it very kind of generic simple, 02:05:24.130 --> 02:05:26.830 align:middle line:84% you can get away with about a dozen parameters, maybe 02:05:26.830 --> 02:05:30.110 align:middle line:84% even a little bit less, but probably you need a dozen. 02:05:30.110 --> 02:05:35.550 align:middle line:84% So I think most of the models you folks have 02:05:35.550 --> 02:05:39.030 align:middle line:84% built have more parameters, probably some of them double 02:05:39.030 --> 02:05:40.030 align:middle line:90% that size. 02:05:40.030 --> 02:05:42.630 align:middle line:84% So that's one of the ideas, to try 02:05:42.630 --> 02:05:45.880 align:middle line:84% to keep things simple to the extent that you can. 02:05:45.880 --> 02:05:50.360 align:middle line:84% Don't introduce parameters if you don't have to. 02:05:50.360 --> 02:05:52.120 align:middle line:84% Then there is this issue of estimation. 02:05:52.120 --> 02:05:56.120 align:middle line:84% That is, the model identifiable with those 12 parameters 02:05:56.120 --> 02:05:57.720 align:middle line:84% and the time series we typically get, 02:05:57.720 --> 02:05:59.660 align:middle line:90% which are on cases and deaths. 02:05:59.660 --> 02:06:02.640 align:middle line:84% Usually those are the two things you can get. 02:06:02.640 --> 02:06:05.940 align:middle line:84% For this model, yes, usually it is identifiable. 02:06:05.940 --> 02:06:08.700 align:middle line:84% That is, most of those parameters you can get. 02:06:08.700 --> 02:06:12.940 align:middle line:84% Although if only cases and deaths, maybe not. 02:06:12.940 --> 02:06:15.860 align:middle line:84% I haven't done this version of the model with vaccination. 02:06:15.860 --> 02:06:17.360 align:middle line:84% The vaccination part makes things 02:06:17.360 --> 02:06:19.680 align:middle line:90% more complex to get to see. 02:06:19.680 --> 02:06:22.040 align:middle line:84% If you have data on vaccination so that you 02:06:22.040 --> 02:06:26.920 align:middle line:84% drive the vaccinated population through the data, 02:06:26.920 --> 02:06:31.320 align:middle line:84% it helps with your ability to estimate the model. 02:06:31.320 --> 02:06:33.360 align:middle line:84% But that's always in the back of my mind 02:06:33.360 --> 02:06:37.960 align:middle line:84% when I do have an empirical leg to the project, that-- 02:06:37.960 --> 02:06:41.560 align:middle line:84% can I estimate this or do I have too many parameters? 02:06:41.560 --> 02:06:42.680 align:middle line:90% Can I simplify it? 02:06:42.680 --> 02:06:45.300 align:middle line:84% Or can we nail down some of the parameters 02:06:45.300 --> 02:06:46.480 align:middle line:90% using other type of data? 02:06:46.480 --> 02:06:49.640 align:middle line:84% Like the fraction of people willing to get vaccinated, 02:06:49.640 --> 02:06:52.120 align:middle line:84% we don't really need to estimate it from this model. 02:06:52.120 --> 02:06:53.962 align:middle line:84% We can look at trends in vaccination, 02:06:53.962 --> 02:06:55.420 align:middle line:84% and what fraction of the population 02:06:55.420 --> 02:06:57.700 align:middle line:84% got vaccinated and second vaccinated. 02:06:57.700 --> 02:07:00.160 align:middle line:84% You can look at surveys, you can look at other sources. 02:07:00.160 --> 02:07:03.020 align:middle line:84% So to the extent that you can pin down some parameters 02:07:03.020 --> 02:07:04.900 align:middle line:90% without using-- 02:07:04.900 --> 02:07:08.560 align:middle line:84% without letting them determine by calibration, do that. 02:07:08.560 --> 02:07:10.100 align:middle line:90% It's another choice. 02:07:10.100 --> 02:07:12.100 align:middle line:90% Sepideh? 02:07:12.100 --> 02:07:16.460 align:middle line:84% AUDIENCE: I was thinking that vaccine efficacy also 02:07:16.460 --> 02:07:17.703 align:middle line:90% is important in this model-- 02:07:17.703 --> 02:07:18.620 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:07:18.620 --> 02:07:20.420 align:middle line:90% AUDIENCE: --because efficacy-- 02:07:20.420 --> 02:07:22.580 align:middle line:84% HAZHIR RAHMANDAD: So vaccine efficacy, 02:07:22.580 --> 02:07:26.460 align:middle line:90% where does it play a role? 02:07:26.460 --> 02:07:31.180 align:middle line:84% What's your intuition for where it is impacting things, Sepideh? 02:07:31.180 --> 02:07:37.260 align:middle line:84% AUDIENCE: So I'm thinking that if we consider vaccine efficacy, 02:07:37.260 --> 02:07:41.150 align:middle line:90% its impact on waning rate. 02:07:41.150 --> 02:07:42.990 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:07:42.990 --> 02:07:46.073 align:middle line:84% So vaccine efficacy is not about waning rate, though there 02:07:46.073 --> 02:07:46.990 align:middle line:90% is something about it. 02:07:46.990 --> 02:07:49.510 align:middle line:84% That is, waning rate is about how long 02:07:49.510 --> 02:07:51.050 align:middle line:90% the vaccine remains effective. 02:07:51.050 --> 02:07:52.130 align:middle line:90% So that's part of it. 02:07:52.130 --> 02:07:53.090 align:middle line:90% That's important. 02:07:53.090 --> 02:07:57.150 align:middle line:84% So the parameter determining the immunity period from vaccine 02:07:57.150 --> 02:08:00.750 align:middle line:84% is an important parameter in assessing 02:08:00.750 --> 02:08:03.270 align:middle line:84% the overall effectiveness of vaccine. 02:08:03.270 --> 02:08:05.910 align:middle line:84% What else is happening here that addresses-- 02:08:05.910 --> 02:08:09.710 align:middle line:84% or what other parameter informs the question of vaccine efficacy 02:08:09.710 --> 02:08:10.210 align:middle line:90% here? 02:08:10.210 --> 02:08:15.150 align:middle line:90% 02:08:15.150 --> 02:08:17.610 align:middle line:90% Anybody else wants to chip in? 02:08:17.610 --> 02:08:18.110 align:middle line:90% Hesam? 02:08:18.110 --> 02:08:21.720 align:middle line:84% AUDIENCE: The color [INAUDIBLE], the two red ones? 02:08:21.720 --> 02:08:23.970 align:middle line:84% HAZHIR RAHMANDAD: Yeah, the two red ones are big ones. 02:08:23.970 --> 02:08:25.790 align:middle line:84% So there is impact of vaccination 02:08:25.790 --> 02:08:32.590 align:middle line:84% on infectivity and impact of vaccination on death rate. 02:08:32.590 --> 02:08:36.930 align:middle line:84% So impact of vaccination on infectivity, this 02:08:36.930 --> 02:08:39.690 align:middle line:84% is determining whether the vaccinated people 02:08:39.690 --> 02:08:45.270 align:middle line:84% are more or less-- how less likely they are to get sick. 02:08:45.270 --> 02:08:48.610 align:middle line:84% So if this parameter is 0, then it 02:08:48.610 --> 02:08:51.690 align:middle line:84% means vaccinated people will not get sick at all. 02:08:51.690 --> 02:08:54.410 align:middle line:84% And if it is 1, it means vaccine doesn't bring down 02:08:54.410 --> 02:08:56.730 align:middle line:84% your risk of getting the disease at all. 02:08:56.730 --> 02:09:00.070 align:middle line:84% And then vaccine impact on death is the other key one. 02:09:00.070 --> 02:09:03.430 align:middle line:84% Again, if it is 1, it means it has no benefits for death. 02:09:03.430 --> 02:09:05.510 align:middle line:84% Once you have got it, and if it is 0, 02:09:05.510 --> 02:09:09.130 align:middle line:84% it means it completely protects against death. 02:09:09.130 --> 02:09:11.050 align:middle line:84% So those are the three parameters really 02:09:11.050 --> 02:09:13.495 align:middle line:84% that matter here in terms of vaccine efficacy. 02:09:13.495 --> 02:09:15.870 align:middle line:84% There is a fourth parameter that is not in Alban's model. 02:09:15.870 --> 02:09:19.730 align:middle line:84% It was in Russ's model, which is the impact of vaccine 02:09:19.730 --> 02:09:22.010 align:middle line:90% on infecting other. 02:09:22.010 --> 02:09:24.750 align:middle line:84% And that is also important in these models. 02:09:24.750 --> 02:09:27.250 align:middle line:84% That's kind of the path through which vaccines protect 02:09:27.250 --> 02:09:30.530 align:middle line:84% the rest of the population, and it's an important factor 02:09:30.530 --> 02:09:32.970 align:middle line:90% in these models. 02:09:32.970 --> 02:09:34.530 align:middle line:90% OK. 02:09:34.530 --> 02:09:36.060 align:middle line:90% Great job. 02:09:36.060 --> 02:09:40.180 align:middle line:90% So keep up the good work. 02:09:40.180 --> 02:09:43.660 align:middle line:84% I think, as you can see, even relatively simple models are not 02:09:43.660 --> 02:09:44.320 align:middle line:90% very simple. 02:09:44.320 --> 02:09:46.287 align:middle line:84% When you're going through the formulations, 02:09:46.287 --> 02:09:48.120 align:middle line:84% there are so many things that are happening. 02:09:48.120 --> 02:09:53.160 align:middle line:84% But kind of process lessons from this exercise, 02:09:53.160 --> 02:09:58.740 align:middle line:84% I hope, keeping things simple to the extent possible, kind 02:09:58.740 --> 02:10:01.300 align:middle line:84% of not trying to add a lot of components. 02:10:01.300 --> 02:10:04.740 align:middle line:84% Especially at your current level of skills, it is hard. 02:10:04.740 --> 02:10:06.540 align:middle line:84% On the one hand, adding details sometimes 02:10:06.540 --> 02:10:10.440 align:middle line:84% make it more operational, makes it easier to deal with it. 02:10:10.440 --> 02:10:13.160 align:middle line:84% On the other hand, it makes it harder to integrate things. 02:10:13.160 --> 02:10:17.620 align:middle line:84% So trying to think hard, What do I really need to add? 02:10:17.620 --> 02:10:19.100 align:middle line:90% becomes important. 02:10:19.100 --> 02:10:22.440 align:middle line:84% Where we are getting the signals for different decisions. 02:10:22.440 --> 02:10:25.280 align:middle line:84% So the decision about perception of risk, 02:10:25.280 --> 02:10:28.200 align:middle line:84% where we are getting the signal is a key decision 02:10:28.200 --> 02:10:31.400 align:middle line:84% in this model, how you are getting it is important. 02:10:31.400 --> 02:10:33.620 align:middle line:84% The other is the signal for vaccination. 02:10:33.620 --> 02:10:36.640 align:middle line:84% How do we decide the number of people 02:10:36.640 --> 02:10:40.640 align:middle line:90% we need to get vaccinated? 02:10:40.640 --> 02:10:43.920 align:middle line:84% You saw that we went through thinking about robustness 02:10:43.920 --> 02:10:44.940 align:middle line:90% of every equation. 02:10:44.940 --> 02:10:47.980 align:middle line:84% Every equation we clicked on, we were thinking in our mind, 02:10:47.980 --> 02:10:51.640 align:middle line:84% OK, how do I enforce the input and output 02:10:51.640 --> 02:10:53.580 align:middle line:90% robustness for this model? 02:10:53.580 --> 02:10:55.480 align:middle line:84% Do I get the right range for inputs, 02:10:55.480 --> 02:10:57.420 align:middle line:84% and does it give the right range for outputs? 02:10:57.420 --> 02:10:59.200 align:middle line:90% And are they logical? 02:10:59.200 --> 02:11:02.580 align:middle line:84% This is very important, and this doesn't come overnight. 02:11:02.580 --> 02:11:05.980 align:middle line:84% You need to be familiar with how these formulations behave. 02:11:05.980 --> 02:11:08.780 align:middle line:84% And that is why we want to work with simple formulations. 02:11:08.780 --> 02:11:11.160 align:middle line:84% The most complex formulations we had here 02:11:11.160 --> 02:11:13.520 align:middle line:84% were those exponential functions that we 02:11:13.520 --> 02:11:17.300 align:middle line:84% looked at in Jason's model, for example. 02:11:17.300 --> 02:11:23.640 align:middle line:84% So let's switch for the last 25 minutes 02:11:23.640 --> 02:11:29.240 align:middle line:84% for our next week's modeling challenge, which 02:11:29.240 --> 02:11:32.260 align:middle line:90% is energy coflows. 02:11:32.260 --> 02:11:35.780 align:middle line:84% So hopefully you have had a chance to look at it. 02:11:35.780 --> 02:11:38.780 align:middle line:84% Basically, this is something that Alexander 02:11:38.780 --> 02:11:39.880 align:middle line:90% is very familiar with. 02:11:39.880 --> 02:11:41.900 align:middle line:84% He has done quite a bit of modeling 02:11:41.900 --> 02:11:47.940 align:middle line:84% with John around coflows and energy and retrofits and so on. 02:11:47.940 --> 02:11:50.500 align:middle line:84% The idea is you want to model buildings 02:11:50.500 --> 02:11:54.860 align:middle line:84% in a city, let's say, and their energy consumption. 02:11:54.860 --> 02:11:59.080 align:middle line:84% So it's a fairly physical problem, 02:11:59.080 --> 02:12:02.460 align:middle line:84% which makes it easier to conceptualize and put numbers 02:12:02.460 --> 02:12:03.080 align:middle line:90% on. 02:12:03.080 --> 02:12:06.500 align:middle line:84% And in the process, we want to learn or improve 02:12:06.500 --> 02:12:10.460 align:middle line:84% your understanding of a key formulation, coflow structures. 02:12:10.460 --> 02:12:14.020 align:middle line:84% So the way the coflow structure works 02:12:14.020 --> 02:12:18.200 align:middle line:84% is that you have the stock that you're tracking-- so buildings. 02:12:18.200 --> 02:12:21.940 align:middle line:84% And then you have some characteristics 02:12:21.940 --> 02:12:24.940 align:middle line:84% of that stock, some characteristics of buildings, 02:12:24.940 --> 02:12:26.000 align:middle line:90% that you need to track. 02:12:26.000 --> 02:12:28.580 align:middle line:84% For example, their energy efficiency. 02:12:28.580 --> 02:12:33.510 align:middle line:84% And that becomes another stock that tracks how energy efficient 02:12:33.510 --> 02:12:37.630 align:middle line:90% the buildings are in that-- 02:12:37.630 --> 02:12:39.050 align:middle line:90% the buildings you are modeling. 02:12:39.050 --> 02:12:42.270 align:middle line:84% So you have the key stock and flow, the main stock 02:12:42.270 --> 02:12:43.650 align:middle line:90% and flow for buildings. 02:12:43.650 --> 02:12:45.670 align:middle line:84% And then you have parallel stock and flow 02:12:45.670 --> 02:12:49.710 align:middle line:84% that is very much parallel to it for energy 02:12:49.710 --> 02:12:52.790 align:middle line:84% efficiency of these buildings, or total cumulative energy 02:12:52.790 --> 02:12:57.790 align:middle line:84% efficiency-- total energy efficiency for those buildings. 02:12:57.790 --> 02:13:00.990 align:middle line:84% And then we want to capture three different effects 02:13:00.990 --> 02:13:01.970 align:middle line:90% in this situation. 02:13:01.970 --> 02:13:04.710 align:middle line:84% One is the vintage effect, which basically 02:13:04.710 --> 02:13:08.330 align:middle line:84% says older buildings have lower energy efficiency. 02:13:08.330 --> 02:13:11.710 align:middle line:84% So as new buildings are introduced, 02:13:11.710 --> 02:13:16.990 align:middle line:84% you will have better technology, better insulation, 02:13:16.990 --> 02:13:20.550 align:middle line:84% less degradation of energy efficiency because 02:13:20.550 --> 02:13:23.010 align:middle line:90% of depreciation and so on. 02:13:23.010 --> 02:13:27.990 align:middle line:84% So all of those make the newer buildings more energy efficient. 02:13:27.990 --> 02:13:29.730 align:middle line:90% You want to capture that. 02:13:29.730 --> 02:13:32.570 align:middle line:84% So that's fairly straightforward. 02:13:32.570 --> 02:13:34.290 align:middle line:90% Then you have retrofits. 02:13:34.290 --> 02:13:36.130 align:middle line:90% So what is a retrofit? 02:13:36.130 --> 02:13:38.910 align:middle line:84% You may go and add insulation to your walls. 02:13:38.910 --> 02:13:40.670 align:middle line:84% You may go and change your windows. 02:13:40.670 --> 02:13:43.310 align:middle line:84% You may go and change your heating system. 02:13:43.310 --> 02:13:49.770 align:middle line:84% You may add these things at the windows and doors that block 02:13:49.770 --> 02:13:55.170 align:middle line:90% the air coming in from cracks. 02:13:55.170 --> 02:13:57.130 align:middle line:84% So there are various ways you can 02:13:57.130 --> 02:14:00.330 align:middle line:84% invest in reducing energy consumption 02:14:00.330 --> 02:14:03.730 align:middle line:84% or increasing energy efficiency of your building. 02:14:03.730 --> 02:14:07.862 align:middle line:84% So capturing that explicitly is important. 02:14:07.862 --> 02:14:09.570 align:middle line:84% That is, you should be able in your model 02:14:09.570 --> 02:14:14.930 align:middle line:84% to change the energy efficiency of these buildings over time 02:14:14.930 --> 02:14:18.470 align:middle line:84% endogenously by investing into retrofits. 02:14:18.470 --> 02:14:20.610 align:middle line:84% So for example, for simplicity, you 02:14:20.610 --> 02:14:23.650 align:middle line:84% can have a rate of investment in retrofits, 02:14:23.650 --> 02:14:30.540 align:middle line:84% and that should turn into some reduction in energy efficiency-- 02:14:30.540 --> 02:14:32.440 align:middle line:84% an increase in energy efficiency, 02:14:32.440 --> 02:14:34.140 align:middle line:90% reduction in energy consumption. 02:14:34.140 --> 02:14:39.080 align:middle line:84% Now, retrofits cannot solve the problem altogether. 02:14:39.080 --> 02:14:42.500 align:middle line:84% They can't drive your energy consumption to 0. 02:14:42.500 --> 02:14:45.000 align:middle line:84% They can improve, but they have limits. 02:14:45.000 --> 02:14:48.460 align:middle line:84% And those limits are partly a function 02:14:48.460 --> 02:14:51.060 align:middle line:84% of the type of a building you have. 02:14:51.060 --> 02:14:55.020 align:middle line:84% So if I have a building that was built in the 1950s with that 02:14:55.020 --> 02:14:59.820 align:middle line:84% technology, how much the retrofit in an economical sense 02:14:59.820 --> 02:15:04.100 align:middle line:84% can go in terms of addressing the energy consumption has 02:15:04.100 --> 02:15:04.940 align:middle line:90% a limit. 02:15:04.940 --> 02:15:07.060 align:middle line:84% So there is a lower bound of energy 02:15:07.060 --> 02:15:09.320 align:middle line:84% consumption per square foot of building, 02:15:09.320 --> 02:15:13.860 align:middle line:84% for example, that each vintage has. 02:15:13.860 --> 02:15:17.380 align:middle line:84% So that needs to be accounted for in your formulation 02:15:17.380 --> 02:15:18.620 align:middle line:90% for retrofits. 02:15:18.620 --> 02:15:22.140 align:middle line:84% And finally, we want to introduce 02:15:22.140 --> 02:15:28.180 align:middle line:84% new technologies that may change that minimum energy consumption. 02:15:28.180 --> 02:15:30.800 align:middle line:84% That is, if now you have a better technology 02:15:30.800 --> 02:15:34.520 align:middle line:84% for retrofitting the insulation in the walls that 02:15:34.520 --> 02:15:38.560 align:middle line:84% makes it cost effective, reasonably economical, 02:15:38.560 --> 02:15:42.500 align:middle line:84% and brings down that threshold significantly, 02:15:42.500 --> 02:15:44.800 align:middle line:84% you want to be able to capture that. 02:15:44.800 --> 02:15:50.560 align:middle line:84% So being able to explicitly have some investment in technology, 02:15:50.560 --> 02:15:57.960 align:middle line:84% or some exogenous technology impacting how far retrofits 02:15:57.960 --> 02:16:00.400 align:middle line:90% can go, becomes key. 02:16:00.400 --> 02:16:03.420 align:middle line:84% So this is the model you need to build. 02:16:03.420 --> 02:16:04.960 align:middle line:84% Basically, a model that allows you 02:16:04.960 --> 02:16:11.680 align:middle line:84% to capture energy consumption of a series of buildings over time, 02:16:11.680 --> 02:16:14.680 align:middle line:84% exposed to different investments in retrofits 02:16:14.680 --> 02:16:17.640 align:middle line:84% and in the technologies that enhance 02:16:17.640 --> 02:16:19.740 align:middle line:90% the effectiveness of retrofits. 02:16:19.740 --> 02:16:22.330 align:middle line:90% 02:16:22.330 --> 02:16:30.370 align:middle line:84% So with that in mind, talk about architectural choices. 02:16:30.370 --> 02:16:32.930 align:middle line:90% So who is a good audience? 02:16:32.930 --> 02:16:35.090 align:middle line:84% Alexander, who was your audience when 02:16:35.090 --> 02:16:37.190 align:middle line:90% you worked on a related topic? 02:16:37.190 --> 02:16:38.510 align:middle line:90% It's not exactly retrofits. 02:16:38.510 --> 02:16:39.910 align:middle line:90% You worked on heat pumps. 02:16:39.910 --> 02:16:41.170 align:middle line:90% But also-- 02:16:41.170 --> 02:16:44.250 align:middle line:84% AUDIENCE: I mean, we include retrofits in our model. 02:16:44.250 --> 02:16:46.770 align:middle line:84% I mean, it's still not done yet, but the hope 02:16:46.770 --> 02:16:49.370 align:middle line:84% was to show this to policymakers. 02:16:49.370 --> 02:16:52.650 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so one possibility is policymakers. 02:16:52.650 --> 02:16:56.510 align:middle line:84% And so how many vintages do you have in your model for this? 02:16:56.510 --> 02:17:00.690 align:middle line:90% 02:17:00.690 --> 02:17:05.090 align:middle line:84% AUDIENCE: So we have from before 1950 all the way till 2050. 02:17:05.090 --> 02:17:07.690 align:middle line:84% And then it's divided into 10-year cohorts 02:17:07.690 --> 02:17:12.250 align:middle line:84% because that's how we could get data on housing efficiency 02:17:12.250 --> 02:17:12.990 align:middle line:90% in areas. 02:17:12.990 --> 02:17:14.323 align:middle line:90% HAZHIR RAHMANDAD: OK, very good. 02:17:14.323 --> 02:17:16.730 align:middle line:84% So note, first of all the level of aggregation is kind 02:17:16.730 --> 02:17:18.309 align:middle line:90% of 10-year cohorts of buildings. 02:17:18.309 --> 02:17:21.650 align:middle line:84% So buildings built in 1950s, 1960s, 1970s, 02:17:21.650 --> 02:17:23.990 align:middle line:90% and so on, are like-- 02:17:23.990 --> 02:17:26.430 align:middle line:84% this is for a policy application. 02:17:26.430 --> 02:17:28.889 align:middle line:84% And partly driven by the availability of data. 02:17:28.889 --> 02:17:30.709 align:middle line:84% If they had more detailed data, maybe they 02:17:30.709 --> 02:17:34.270 align:middle line:84% would have broken it down into smaller cohorts as well. 02:17:34.270 --> 02:17:40.150 align:middle line:84% For our purpose, we are doing this more for learning purposes 02:17:40.150 --> 02:17:43.170 align:middle line:84% and at a higher level of aggregation. 02:17:43.170 --> 02:17:46.889 align:middle line:84% So I'm telling you to use only three cohorts, or three stocks, 02:17:46.889 --> 02:17:49.010 align:middle line:84% basically, of buildings of different ages. 02:17:49.010 --> 02:17:52.930 align:middle line:84% So this should keep your life easier. 02:17:52.930 --> 02:17:56.110 align:middle line:90% 02:17:56.110 --> 02:18:00.190 align:middle line:84% But it is conceptually very similar 02:18:00.190 --> 02:18:03.969 align:middle line:84% to the kind of a model that can go to the policy level. 02:18:03.969 --> 02:18:05.490 align:middle line:90% You just add more cohorts. 02:18:05.490 --> 02:18:08.709 align:middle line:90% 02:18:08.709 --> 02:18:12.330 align:middle line:84% Then as you build the model, try to keep it in equilibrium. 02:18:12.330 --> 02:18:16.870 align:middle line:90% That is, given a rate of-- 02:18:16.870 --> 02:18:22.340 align:middle line:84% I'm not sure how equilibriumy this model is. 02:18:22.340 --> 02:18:25.440 align:middle line:90% 02:18:25.440 --> 02:18:27.980 align:middle line:84% So if you have retrofits happening-- that is, 02:18:27.980 --> 02:18:30.000 align:middle line:90% you're investing in retrofits-- 02:18:30.000 --> 02:18:33.480 align:middle line:84% by definition, the energy efficiency 02:18:33.480 --> 02:18:39.740 align:middle line:84% is improving for each of the stocks over time. 02:18:39.740 --> 02:18:43.400 align:middle line:90% 02:18:43.400 --> 02:18:48.600 align:middle line:84% So it may not be even meaningful to have an equilibrium. 02:18:48.600 --> 02:18:53.320 align:middle line:84% So make sure it is in equilibrium without retrofits 02:18:53.320 --> 02:18:56.240 align:middle line:84% happening, because with retrofits happening, 02:18:56.240 --> 02:19:01.000 align:middle line:84% it becomes infeasible to have equilibrium unless you have 02:19:01.000 --> 02:19:03.480 align:middle line:84% saturated-- that is, you have basically 02:19:03.480 --> 02:19:06.680 align:middle line:84% used all the retrofits possible, and then it is not 02:19:06.680 --> 02:19:09.719 align:middle line:90% having an impact anymore. 02:19:09.719 --> 02:19:14.120 align:middle line:84% AUDIENCE: Just making sure I understand how this works. 02:19:14.120 --> 02:19:17.700 align:middle line:84% So the vintage effect, that's the characteristic 02:19:17.700 --> 02:19:19.360 align:middle line:90% of the building. 02:19:19.360 --> 02:19:24.260 align:middle line:84% It's not like how I was [INAUDIBLE] is like, 02:19:24.260 --> 02:19:27.820 align:middle line:90% if they're built in the 1950s. 02:19:27.820 --> 02:19:32.100 align:middle line:84% Depending on the time span of the model, do they age? 02:19:32.100 --> 02:19:35.400 align:middle line:84% Do the buildings age into different layers of vintage, 02:19:35.400 --> 02:19:39.700 align:middle line:84% or is it just with them by birth? 02:19:39.700 --> 02:19:42.879 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so this is actually a good question, 02:19:42.879 --> 02:19:45.260 align:middle line:90% and a bit of a tricky one. 02:19:45.260 --> 02:19:48.680 align:middle line:84% That is, you can have three stocks, 02:19:48.680 --> 02:19:51.980 align:middle line:84% let's say, for three groupings of buildings. 02:19:51.980 --> 02:19:55.940 align:middle line:84% So then you can have buildings come into it in the 1950s, 02:19:55.940 --> 02:19:58.440 align:middle line:84% and then other buildings coming in 1960s, 02:19:58.440 --> 02:20:01.780 align:middle line:84% other buildings coming in 1970s, and then they age and go through 02:20:01.780 --> 02:20:02.380 align:middle line:90% this. 02:20:02.380 --> 02:20:04.900 align:middle line:84% So at any point in time, depending on varying 02:20:04.900 --> 02:20:08.340 align:middle line:84% the simulation time you are, you may have 1950s buildings 02:20:08.340 --> 02:20:11.460 align:middle line:90% in here, or in here, or in here. 02:20:11.460 --> 02:20:13.830 align:middle line:84% So that becomes-- and then how do you 02:20:13.830 --> 02:20:18.390 align:middle line:84% track that their characteristics carry over with them? 02:20:18.390 --> 02:20:21.270 align:middle line:84% So the tracking of the characteristics 02:20:21.270 --> 02:20:23.070 align:middle line:90% is through the coflows. 02:20:23.070 --> 02:20:25.610 align:middle line:84% Basically, that's what the coflows do for you. 02:20:25.610 --> 02:20:28.630 align:middle line:90% 02:20:28.630 --> 02:20:31.650 align:middle line:84% And yes, that's how you would do it. 02:20:31.650 --> 02:20:34.010 align:middle line:84% In this case, just have three groupings. 02:20:34.010 --> 02:20:38.470 align:middle line:84% So it is not that this stock is always the 1950s buildings 02:20:38.470 --> 02:20:40.790 align:middle line:84% in the way we are building it in this model. 02:20:40.790 --> 02:20:42.490 align:middle line:90% You could do it differently. 02:20:42.490 --> 02:20:47.570 align:middle line:84% That is, you don't change these buildings, their cohorts. 02:20:47.570 --> 02:20:49.590 align:middle line:84% So you would have actually two layers. 02:20:49.590 --> 02:20:52.630 align:middle line:84% One is the age, so going to the right 02:20:52.630 --> 02:20:54.670 align:middle line:90% is the age of the building. 02:20:54.670 --> 02:20:57.590 align:middle line:84% And then the other one is the cohort that you have. 02:20:57.590 --> 02:21:00.970 align:middle line:84% That this, this is the cohort of 1950s is aging this way. 02:21:00.970 --> 02:21:03.950 align:middle line:84% And the cohort of 1960s-- that is the more correct way, 02:21:03.950 --> 02:21:06.230 align:middle line:90% or more-- 02:21:06.230 --> 02:21:09.390 align:middle line:84% but it is a little bit too complex for our purpose. 02:21:09.390 --> 02:21:10.490 align:middle line:90% How did you guys do it? 02:21:10.490 --> 02:21:13.270 align:middle line:84% AUDIENCE: We had separate stocks for every single cohort. 02:21:13.270 --> 02:21:14.710 align:middle line:90% And then we track-- 02:21:14.710 --> 02:21:15.210 align:middle line:90% sorry? 02:21:15.210 --> 02:21:16.960 align:middle line:84% AUDIENCE: And age them, too, through time? 02:21:16.960 --> 02:21:18.085 align:middle line:90% AUDIENCE: What do you mean? 02:21:18.085 --> 02:21:19.590 align:middle line:84% AUDIENCE: Like a specific cohort, 02:21:19.590 --> 02:21:22.610 align:middle line:84% if the span of your model is going for 30 years, 02:21:22.610 --> 02:21:23.630 align:middle line:90% will they deteriorate? 02:21:23.630 --> 02:21:24.610 align:middle line:90% Their condition deteriorate? 02:21:24.610 --> 02:21:26.530 align:middle line:84% AUDIENCE: No, we actually don't include that, 02:21:26.530 --> 02:21:28.590 align:middle line:84% because I guess we could, and we actually 02:21:28.590 --> 02:21:30.090 align:middle line:84% do track the different cohorts' age. 02:21:30.090 --> 02:21:31.310 align:middle line:90% Like that is a coflow. 02:21:31.310 --> 02:21:34.010 align:middle line:84% But we don't-- that has no effect on the rest of the model 02:21:34.010 --> 02:21:35.097 align:middle line:90% because-- 02:21:35.097 --> 02:21:36.430 align:middle line:90% I actually never discussed that. 02:21:36.430 --> 02:21:38.970 align:middle line:84% But I think just data wise, it would 02:21:38.970 --> 02:21:40.950 align:middle line:84% be almost impossible to see those effects. 02:21:40.950 --> 02:21:45.970 align:middle line:84% Getting efficiency data, even for 2020 was hard, much less 02:21:45.970 --> 02:21:47.230 align:middle line:90% getting a time series of it. 02:21:47.230 --> 02:21:48.188 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 02:21:48.188 --> 02:21:50.910 align:middle line:84% So this is an important architectural choice, 02:21:50.910 --> 02:21:53.697 align:middle line:84% so I want everybody to follow what we are talking about. 02:21:53.697 --> 02:21:55.030 align:middle line:90% So there are two different ways. 02:21:55.030 --> 02:21:58.450 align:middle line:84% One is to capture the aging of buildings 02:21:58.450 --> 02:22:01.870 align:middle line:84% and think of cohorts to be happening with that aging. 02:22:01.870 --> 02:22:05.930 align:middle line:84% That is, I'm feeding the 1950s cohorts into the first set 02:22:05.930 --> 02:22:06.570 align:middle line:90% of stocks. 02:22:06.570 --> 02:22:10.730 align:middle line:84% 10 years later, I'm feeding the 1960s cohort in the first set, 02:22:10.730 --> 02:22:14.490 align:middle line:84% and this first set is now going to the second set of stocks, 02:22:14.490 --> 02:22:15.790 align:middle line:90% and so on. 02:22:15.790 --> 02:22:20.110 align:middle line:84% The other is to say, no, I have different stocks and flows 02:22:20.110 --> 02:22:21.710 align:middle line:90% for each of these cohorts. 02:22:21.710 --> 02:22:24.790 align:middle line:84% So for the 1950s houses, I feed them. 02:22:24.790 --> 02:22:27.970 align:middle line:84% And then when I get to the 1960s in my simulation, 02:22:27.970 --> 02:22:31.130 align:middle line:84% I go to the second set of buildings, feed that group. 02:22:31.130 --> 02:22:34.290 align:middle line:84% And then when I go to the 1970s, I feed the third group. 02:22:34.290 --> 02:22:38.030 align:middle line:84% And then if I care about aging separately, 02:22:38.030 --> 02:22:41.990 align:middle line:84% I would have separate stocks and flows for 1950s homes that are 02:22:41.990 --> 02:22:45.990 align:middle line:84% 10 years old, and then 20 year old, and 30 year old, and so on. 02:22:45.990 --> 02:22:50.010 align:middle line:84% So Alexander's approach in their work has been separate cohorts, 02:22:50.010 --> 02:22:52.010 align:middle line:90% but don't worry about aging. 02:22:52.010 --> 02:22:53.910 align:middle line:84% There is probably some deterioration, 02:22:53.910 --> 02:22:56.450 align:middle line:84% demolishing, long term that you just have. 02:22:56.450 --> 02:22:56.710 align:middle line:90% AUDIENCE: We have demolition. 02:22:56.710 --> 02:22:58.668 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so you have demolition. 02:22:58.668 --> 02:23:03.588 align:middle line:84% But do you have a higher-order delay for that? 02:23:03.588 --> 02:23:04.130 align:middle line:90% AUDIENCE: No. 02:23:04.130 --> 02:23:04.410 align:middle line:90% HAZHIR RAHMANDAD: No. 02:23:04.410 --> 02:23:07.010 align:middle line:84% So you just have the first-order draining of that. 02:23:07.010 --> 02:23:07.560 align:middle line:84% AUDIENCE: Yeah, we don't have any hierarchy. 02:23:07.560 --> 02:23:08.260 align:middle line:90% HAZHIR RAHMANDAD: That's OK. 02:23:08.260 --> 02:23:09.160 align:middle line:84% AUDIENCE: And then obviously, like we 02:23:09.160 --> 02:23:10.740 align:middle line:90% use subscripts for everything. 02:23:10.740 --> 02:23:11.000 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 02:23:11.000 --> 02:23:12.160 align:middle line:90% AUDIENCE: And so like-- 02:23:12.160 --> 02:23:13.220 align:middle line:84% AUDIENCE: So [INAUDIBLE] can look at it. 02:23:13.220 --> 02:23:13.720 align:middle line:90% AUDIENCE: That's right, yeah. 02:23:13.720 --> 02:23:15.160 align:middle line:84% AUDIENCE: Because if you don't, then it's-- 02:23:15.160 --> 02:23:17.640 align:middle line:84% AUDIENCE: Then it's-- yeah, we have whatever eight or nine 02:23:17.640 --> 02:23:18.140 align:middle line:90% cohorts. 02:23:18.140 --> 02:23:19.807 align:middle line:84% HAZHIR RAHMANDAD: Honestly, you could go 02:23:19.807 --> 02:23:21.020 align:middle line:90% with either of these choices. 02:23:21.020 --> 02:23:24.860 align:middle line:84% I think the impact is minimal in our purposes. 02:23:24.860 --> 02:23:31.400 align:middle line:84% But I like to have the continuity over aging process 02:23:31.400 --> 02:23:34.720 align:middle line:84% to be separated so that it kind of you 02:23:34.720 --> 02:23:39.200 align:middle line:84% practice the coflow structures' nuances, a little bit more 02:23:39.200 --> 02:23:41.320 align:middle line:90% with that structure. 02:23:41.320 --> 02:23:46.000 align:middle line:84% So what that means is feed the model the 1950s building rate, 02:23:46.000 --> 02:23:48.280 align:middle line:84% and the 1960s building rate, and so on. 02:23:48.280 --> 02:23:49.760 align:middle line:84% AUDIENCE: One aging chain that goes 02:23:49.760 --> 02:23:51.100 align:middle line:90% through the different lineages? 02:23:51.100 --> 02:23:55.400 align:middle line:84% HAZHIR RAHMANDAD: Yeah, and just have three different stocks, 02:23:55.400 --> 02:23:56.680 align:middle line:90% basically. 02:23:56.680 --> 02:24:02.000 align:middle line:84% So that's kind of the key architectural choice 02:24:02.000 --> 02:24:04.700 align:middle line:84% at the beginning for vintage versus aging. 02:24:04.700 --> 02:24:06.980 align:middle line:84% And I think kind of you're combining them together 02:24:06.980 --> 02:24:09.540 align:middle line:84% into a single stock and flow chain. 02:24:09.540 --> 02:24:12.300 align:middle line:84% Then there is the question of what other stocks 02:24:12.300 --> 02:24:16.780 align:middle line:84% you would need to capture what we are trying to do. 02:24:16.780 --> 02:24:20.180 align:middle line:84% And here, I want you to actually go and deal 02:24:20.180 --> 02:24:22.060 align:middle line:90% with that challenge yourself. 02:24:22.060 --> 02:24:28.700 align:middle line:84% But a hint is that if you need to-- if you need memory 02:24:28.700 --> 02:24:33.220 align:middle line:84% for something that in the system is changing, 02:24:33.220 --> 02:24:37.020 align:middle line:84% you will need some stock to keep track of that memory. 02:24:37.020 --> 02:24:40.860 align:middle line:84% If something is not changing, then it is a parameter. 02:24:40.860 --> 02:24:43.360 align:middle line:90% So that distinction is key. 02:24:43.360 --> 02:24:44.860 align:middle line:84% There are things that are parameters 02:24:44.860 --> 02:24:45.880 align:middle line:90% that are not changing. 02:24:45.880 --> 02:24:48.040 align:middle line:84% And then there are things that need to change. 02:24:48.040 --> 02:24:52.260 align:middle line:84% And you need to be able to calculate-- to observe them, 02:24:52.260 --> 02:24:54.780 align:middle line:84% and that they will call for stocks. 02:24:54.780 --> 02:24:57.580 align:middle line:84% See how that kind of works for you. 02:24:57.580 --> 02:25:04.750 align:middle line:84% Then the last part is thinking about performance tests 02:25:04.750 --> 02:25:06.290 align:middle line:90% for this model. 02:25:06.290 --> 02:25:07.910 align:middle line:84% That is, when do you have a model 02:25:07.910 --> 02:25:11.350 align:middle line:84% that you are kind of satisfied with based 02:25:11.350 --> 02:25:14.430 align:middle line:84% on the objectives of this exercise? 02:25:14.430 --> 02:25:18.490 align:middle line:84% So what are some of the tests that come to your mind? 02:25:18.490 --> 02:25:35.750 align:middle line:90% 02:25:35.750 --> 02:25:38.150 align:middle line:90% Any takers? 02:25:38.150 --> 02:25:39.648 align:middle line:84% AUDIENCE: Extreme condition tests. 02:25:39.648 --> 02:25:41.190 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so what would 02:25:41.190 --> 02:25:44.170 align:middle line:84% be a good extreme condition test in this case? 02:25:44.170 --> 02:26:04.970 align:middle line:90% 02:26:04.970 --> 02:26:07.230 align:middle line:84% So maybe before even extreme conditions, 02:26:07.230 --> 02:26:12.190 align:middle line:84% think about what are the inputs and outputs in this structure? 02:26:12.190 --> 02:26:13.150 align:middle line:90% So what are the inputs? 02:26:13.150 --> 02:26:14.270 align:middle line:90% What are the outputs? 02:26:14.270 --> 02:26:18.513 align:middle line:90% 02:26:18.513 --> 02:26:19.930 align:middle line:84% AUDIENCE: Seeing what would happen 02:26:19.930 --> 02:26:22.635 align:middle line:84% if you built a million buildings [INAUDIBLE]. 02:26:22.635 --> 02:26:23.510 align:middle line:90% HAZHIR RAHMANDAD: OK. 02:26:23.510 --> 02:26:28.070 align:middle line:90% So building of new buildings. 02:26:28.070 --> 02:26:31.890 align:middle line:90% That's a potential input. 02:26:31.890 --> 02:26:32.850 align:middle line:90% Yep. 02:26:32.850 --> 02:26:33.630 align:middle line:90% What else? 02:26:33.630 --> 02:26:38.098 align:middle line:90% 02:26:38.098 --> 02:26:40.690 align:middle line:84% AUDIENCE: You can think about like you're raising 02:26:40.690 --> 02:26:42.853 align:middle line:90% the ceiling of efficiency. 02:26:42.853 --> 02:26:43.770 align:middle line:90% HAZHIR RAHMANDAD: Yep. 02:26:43.770 --> 02:26:50.090 align:middle line:84% Investment in efficiency technology. 02:26:50.090 --> 02:26:51.130 align:middle line:90% AUDIENCE: Right. 02:26:51.130 --> 02:26:52.850 align:middle line:84% HAZHIR RAHMANDAD: So introduction 02:26:52.850 --> 02:26:56.250 align:middle line:90% of new technologies. 02:26:56.250 --> 02:26:58.012 align:middle line:90% What else? 02:26:58.012 --> 02:26:59.780 align:middle line:84% AUDIENCE: Investment in [? retrofits. ?] 02:26:59.780 --> 02:27:01.530 align:middle line:84% HAZHIR RAHMANDAD: Investment in retrofits. 02:27:01.530 --> 02:27:05.660 align:middle line:90% 02:27:05.660 --> 02:27:10.027 align:middle line:84% So those three, I think are the biggest inputs for this module. 02:27:10.027 --> 02:27:11.860 align:middle line:84% And this would be a module that you actually 02:27:11.860 --> 02:27:13.700 align:middle line:84% can use in a lot of different models, that 02:27:13.700 --> 02:27:16.460 align:middle line:84% are kind of the core ideas, very much applicable 02:27:16.460 --> 02:27:17.860 align:middle line:90% to a lot of other settings. 02:27:17.860 --> 02:27:20.940 align:middle line:90% Then let's think about outputs. 02:27:20.940 --> 02:27:22.280 align:middle line:90% What do you care about? 02:27:22.280 --> 02:27:25.180 align:middle line:90% 02:27:25.180 --> 02:27:27.580 align:middle line:84% AUDIENCE: Total energy consumption. 02:27:27.580 --> 02:27:28.760 align:middle line:90% Total energy consumption. 02:27:28.760 --> 02:27:33.740 align:middle line:84% HAZHIR RAHMANDAD: Yeah, so total energy consumption. 02:27:33.740 --> 02:27:43.540 align:middle line:84% And then per square feet energy consumption, because you also 02:27:43.540 --> 02:27:45.100 align:middle line:84% may care about the normalized one 02:27:45.100 --> 02:27:48.840 align:middle line:84% if you are changing the inflow of the stocks. 02:27:48.840 --> 02:27:52.200 align:middle line:90% 02:27:52.200 --> 02:27:54.460 align:middle line:84% AUDIENCE: Is that what we're calling efficiency 02:27:54.460 --> 02:27:55.880 align:middle line:90% per square foot consumption? 02:27:55.880 --> 02:27:59.240 align:middle line:84% HAZHIR RAHMANDAD: Yeah, basically, or its reverse 02:27:59.240 --> 02:28:01.386 align:middle line:90% of efficiency [INAUDIBLE]. 02:28:01.386 --> 02:28:05.760 align:middle line:90% 02:28:05.760 --> 02:28:06.740 align:middle line:90% Anything else? 02:28:06.740 --> 02:28:12.320 align:middle line:90% 02:28:12.320 --> 02:28:14.600 align:middle line:90% AUDIENCE: Demolitions or-- 02:28:14.600 --> 02:28:16.960 align:middle line:84% HAZHIR RAHMANDAD: Perhaps, but they're 02:28:16.960 --> 02:28:21.000 align:middle line:90% probably not that critical. 02:28:21.000 --> 02:28:23.880 align:middle line:84% Another thing might be, I think, relevant here 02:28:23.880 --> 02:28:28.500 align:middle line:84% is efficiency of investments in retrofits. 02:28:28.500 --> 02:28:35.800 align:middle line:90% 02:28:35.800 --> 02:28:36.860 align:middle line:90% What does that mean? 02:28:36.860 --> 02:28:44.500 align:middle line:84% It means I'm investing $1, how much gain in energy efficiency 02:28:44.500 --> 02:28:45.500 align:middle line:90% I'm getting out of that. 02:28:45.500 --> 02:28:49.640 align:middle line:84% That's kind of marginal utility or benefit is key for decisions 02:28:49.640 --> 02:28:52.440 align:middle line:84% that you will build into these types of models. 02:28:52.440 --> 02:28:55.670 align:middle line:84% You guys also deal with that, I think, somewhere in your model. 02:28:55.670 --> 02:28:58.450 align:middle line:90% 02:28:58.450 --> 02:29:00.410 align:middle line:90% AUDIENCE: I'm trying to think. 02:29:00.410 --> 02:29:09.050 align:middle line:84% We do-- We actually don't talk about retrofit technology 02:29:09.050 --> 02:29:09.633 align:middle line:90% all that much. 02:29:09.633 --> 02:29:11.883 align:middle line:84% HAZHIR RAHMANDAD: So this is not about the technology. 02:29:11.883 --> 02:29:15.150 align:middle line:84% This is about the decisions for each cohort or each group, 02:29:15.150 --> 02:29:18.177 align:middle line:84% whether to invest in retrofit or not. 02:29:18.177 --> 02:29:19.010 align:middle line:90% AUDIENCE: So we do-- 02:29:19.010 --> 02:29:20.930 align:middle line:84% yeah, so we do have an endogenous 02:29:20.930 --> 02:29:21.930 align:middle line:90% like optimal efficiency. 02:29:21.930 --> 02:29:23.013 align:middle line:90% HAZHIR RAHMANDAD: Exactly. 02:29:23.013 --> 02:29:24.810 align:middle line:84% So that's what I'm saying, that if you 02:29:24.810 --> 02:29:28.370 align:middle line:84% want to calculate optimal efficiency investments, 02:29:28.370 --> 02:29:31.250 align:middle line:84% you need to be able to see the marginal value. 02:29:31.250 --> 02:29:34.090 align:middle line:84% Or if you are investing this how, 02:29:34.090 --> 02:29:37.510 align:middle line:84% much you are getting out of it to then inform 02:29:37.510 --> 02:29:39.010 align:middle line:84% whether you increase your investment 02:29:39.010 --> 02:29:41.610 align:middle line:90% or decrease your investment. 02:29:41.610 --> 02:29:43.690 align:middle line:84% AUDIENCE: So by efficiency, do you essentially 02:29:43.690 --> 02:29:44.932 align:middle line:90% mean more like profitability? 02:29:44.932 --> 02:29:45.890 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 02:29:45.890 --> 02:29:52.170 align:middle line:84% So basically, it turns into I invest this amount of dollar, 02:29:52.170 --> 02:29:57.230 align:middle line:84% I change my efficiency in units of energy per square foot 02:29:57.230 --> 02:29:58.210 align:middle line:90% by this much. 02:29:58.210 --> 02:30:00.910 align:middle line:84% Then you multiply that by the price of energy, 02:30:00.910 --> 02:30:03.130 align:middle line:84% and so on, and your total energy consumption, 02:30:03.130 --> 02:30:04.090 align:middle line:90% and you can do that. 02:30:04.090 --> 02:30:06.050 align:middle line:84% Now, you guys don't need to do any of those. 02:30:06.050 --> 02:30:09.530 align:middle line:84% I'm just saying why this is an important output to track, 02:30:09.530 --> 02:30:13.850 align:middle line:84% not that you need to do the calculations for optimal energy. 02:30:13.850 --> 02:30:16.990 align:middle line:84% AUDIENCE: One quick clarifying question. 02:30:16.990 --> 02:30:21.470 align:middle line:84% To reap the benefits of investment in efficiency, 02:30:21.470 --> 02:30:25.190 align:middle line:90% we require retrofit, right? 02:30:25.190 --> 02:30:27.790 align:middle line:84% HAZHIR RAHMANDAD: Yes, some level of retrofit. 02:30:27.790 --> 02:30:30.330 align:middle line:84% AUDIENCE: I guess-- so just for conceptual clarity. 02:30:30.330 --> 02:30:34.870 align:middle line:84% So if retrofit happens at time t of a given level, 02:30:34.870 --> 02:30:38.110 align:middle line:90% that efficiency, that persists. 02:30:38.110 --> 02:30:43.753 align:middle line:84% And then in the future retrofit happening at t plus n-- 02:30:43.753 --> 02:30:44.670 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:30:44.670 --> 02:30:45.110 align:middle line:90% AUDIENCE: [INAUDIBLE] 02:30:45.110 --> 02:30:46.027 align:middle line:90% HAZHIR RAHMANDAD: Yes. 02:30:46.027 --> 02:30:47.830 align:middle line:84% So the retrofit, when it happens, 02:30:47.830 --> 02:30:51.320 align:middle line:84% it brings up the efficiency or brings down the consumption 02:30:51.320 --> 02:30:53.142 align:middle line:90% of energy per square foot. 02:30:53.142 --> 02:30:54.600 align:middle line:84% AUDIENCE: Just wanted to understand 02:30:54.600 --> 02:30:55.767 align:middle line:90% how those two are connected. 02:30:55.767 --> 02:30:57.120 align:middle line:90% HAZHIR RAHMANDAD: Yeah. 02:30:57.120 --> 02:30:58.320 align:middle line:90% OK. 02:30:58.320 --> 02:31:01.920 align:middle line:84% I think those are probably a good coverage of the key inputs 02:31:01.920 --> 02:31:03.200 align:middle line:90% and outputs. 02:31:03.200 --> 02:31:08.400 align:middle line:84% So then in thinking about extreme conditions, 02:31:08.400 --> 02:31:15.600 align:middle line:84% probably if you are investing in efficiency, you don't want-- 02:31:15.600 --> 02:31:18.000 align:middle line:84% if you're investing in retrofits, 02:31:18.000 --> 02:31:20.560 align:middle line:84% you don't want your energy consumption to go up. 02:31:20.560 --> 02:31:24.080 align:middle line:84% That's kind of simple basic things like that. 02:31:24.080 --> 02:31:28.000 align:middle line:84% They should be trivial, but your model should also not 02:31:28.000 --> 02:31:30.340 align:middle line:90% fail on things like that. 02:31:30.340 --> 02:31:37.640 align:middle line:84% You don't want energy efficiency to go below the minimum feasible 02:31:37.640 --> 02:31:43.320 align:middle line:84% given the current vintage, whatever you have. 02:31:43.320 --> 02:31:48.120 align:middle line:90% So that's another consideration. 02:31:48.120 --> 02:32:02.680 align:middle line:84% So energy efficiency remain above minimum for vintage. 02:32:02.680 --> 02:32:07.380 align:middle line:90% 02:32:07.380 --> 02:32:15.860 align:middle line:84% If you invest in retrofits, energy consumption 02:32:15.860 --> 02:32:23.140 align:middle line:84% per square foot should not increase. 02:32:23.140 --> 02:32:28.300 align:middle line:84% And I should just make this a little bit smaller. 02:32:28.300 --> 02:32:30.380 align:middle line:84% There are other things that you can 02:32:30.380 --> 02:32:33.680 align:middle line:84% think of on the extreme condition tests? 02:32:33.680 --> 02:32:43.020 align:middle line:90% 02:32:43.020 --> 02:32:45.220 align:middle line:90% OK. 02:32:45.220 --> 02:32:46.780 align:middle line:90% This is a starting point. 02:32:46.780 --> 02:32:49.950 align:middle line:90% So is the task clear? 02:32:49.950 --> 02:32:52.830 align:middle line:84% You're building a model of retrofits 02:32:52.830 --> 02:33:00.510 align:middle line:84% that hopefully captures the requirements and is robust, 02:33:00.510 --> 02:33:03.870 align:middle line:84% and you test it with a few of these inputs and outputs. 02:33:03.870 --> 02:33:05.870 align:middle line:84% Try to put the model in equilibrium 02:33:05.870 --> 02:33:09.350 align:middle line:84% when there is no investment in retrofits. 02:33:09.350 --> 02:33:11.590 align:middle line:84% When there is investment in retrofits, by definition, 02:33:11.590 --> 02:33:13.610 align:middle line:90% it wouldn't be in equilibrium. 02:33:13.610 --> 02:33:16.230 align:middle line:90% 02:33:16.230 --> 02:33:18.410 align:middle line:84% And when there is no change in technology. 02:33:18.410 --> 02:33:20.430 align:middle line:84% But then, you should change the technology 02:33:20.430 --> 02:33:24.470 align:middle line:84% and you should change the retrofit levels or investment 02:33:24.470 --> 02:33:26.270 align:middle line:90% levels. 02:33:26.270 --> 02:33:26.830 align:middle line:90% Great. 02:33:26.830 --> 02:33:30.090 align:middle line:90% Any questions? 02:33:30.090 --> 02:33:30.590 align:middle line:90% OK. 02:33:30.590 --> 02:33:38.430 align:middle line:84% So anybody online-- any questions that you guys have? 02:33:38.430 --> 02:33:39.110 align:middle line:90% OK. 02:33:39.110 --> 02:33:40.410 align:middle line:90% Thanks so much, folks. 02:33:40.410 --> 02:33:42.900 align:middle line:90% And see you next week. 02:33:42.900 --> 02:33:46.000 align:middle line:90%