PROFESSOR: So let's go through, now,
how we can parameterize our guideline specifically
for COVID-19 by looking at specific superspreading events.
So the event that was analyzed in great detail first,
and which is going to be of most use for us
initially for parameterizing the guideline,
is the Skajit Valley Chorale superspreading incident.
So this was, again, a 2 and 1/2 hour choir practice
involving 61 people, one of whom was known to be infected.
The practice lasted 2 and 1/2 hours.
And in the end, there were 53 infected people, two of whom
later died.
So this was a large room with a height of 4 and 1/2 meters
and an area of 180 meters squared.
It was poorly ventilated.
The heat was on for a certain amount of time
and then taken off.
And the average air change rate was estimated at 0.65 per hour.
And of course, the people were singing for much of the time,
leading to much higher rates of droplet emission.
And in fact, I think we can assume for this event, given
the huge number of infections that
occurred in such a short time, that the index patient--
the index case-- was at near the peak viral load,
peak of infection.
And also, that allows us to make a conservative estimate
of using that for calibrating our guideline.
So if we look at the figure here,
we can see the droplet distributions
taken from experimental measurements
of Morawska et al in 2009.
And those droplet distributions have been fed into the model
that we just described and evolved in time
in such a way that corresponds to the conditions of the Skajit
Valley Choir itself.
And so what we can see is that the droplet distribution
corresponding to singing--
or the closest approximation of singing,
which are measurements of voiced aahs
from the original experiment--
that distribution is much bigger than all the others.
It has a very broad tail to somewhat larger sizes.
But it has a peak just below 1 micron.
Similarly, the other types of activities
measured in the original study, which
correspond to, for example, whispered ahh or speaking
or in counting of numbers, for example,
or various forms of breathing through the nose and the mouth
or only through the nose--
all those distributions have much lower sort of magnitude
or number of drops.
And this is also drop volume.
We have accounted for the size of the drops as well.
So it's the total droplet volume per total volume or volume
fraction.
And the peak of all the distributions
is in a similar place, just below 1 micron,
so again, corresponding to the aerosol range.
And it's important that we take those droplet distributions
and evolve them in the Skajit Valley Choir space.
So then, we can figure out which of those droplets
survived and would be in the air and would be then corresponding
to the airborne transmission and can
be compared with the actual spreading events that occurred
using the Wells-Riley model.
So is it a short amount of time?
We're going to assume there was no delay caused by incubation.
But rather, people were getting infected but not passing it
on to anybody else.
And so we will use the Wells-Riley model.
So when we do that fitting, we come out
with a value of Cq, the number of infection quanta per volume
in the exhaled breath of the infected person,
around 900 quanta per meter cubed.
A published study of Miller et al
came to a similar conclusion of 870 quanta per meters cubed.
And so we can take that to be a reasonable value for singing.
Now, if we go to the next figure,
we can include all of these estimated total quanta
concentrations corresponding to different hypothetical forms
of respiration in the Skajit Valley Choir
and use that for rescaling.
So we can say, the choir was actually involving singing.
And that gave us a number around 900.
And then if we rescale, the other amounts
of respiratory droplets corresponding
to different activities would have correspondingly scaled
values of Cq.
And as a further calibration, we can compare it
with another recent study of Asadi and Ristenpart,
where again, different types of respiratory activities
were measured for their aerosol size distributions,
including speaking at different levels of volume
and also breathing in different ways.
And if we line up two values that
correspond to sort of intermediate speech
as a calibration, then we find that the quanta
values that we infer--
the Cq values-- for both of those independent studies
of respiratory droplets really correlate nicely
across different types of activities
from breathing to speaking to singing,
allowing us a consistent definition of Cq,
again, for a situation corresponding
to most likely peak infectivity.
So we are talking about sort of the worst case
scenario in order to derive a conservative guideline.
It should also be noted that the median age of the choir members
was 69.
And by using this spreading incident,
we are again being conservative, because it is well established
that elderly persons have an elevated risk of complications
and even death from COVID-19, and perhaps also
some evidence showing increased risk of transmission.
So therefore, when we apply the guideline
to a general population, including
younger and healthy people, that we
will find that we are making a conservative estimate,
which is our goal.
So at this point, we have a fully parameterized guideline.
And we have consistent values of Cq
across a range of respiratory activities
involving two different studies of respiratory aerosols,
all coming from the Skajit Choir incident.
So now, let's look at some other spreading incidents
to see if we can get consistent values of Cq
in cases where people were not singing
and where the size of the room was different,
and sort of see if we really have
a transferable inference here.
And if we do find consistent numbers,
it provides further evidence to support
the hypothesis of airborne transmission
in all of these cases.
So the next example we'll look at
is the incident of the Tiantong Temple religious ceremony
and, in particular, the buses that went back and forth
from that ceremony.
One bus, in particular, was similar to this Dongfeng tour
bus luxury liner, which underwent
a 100-minute trip to Ningbo and then back in the same seating.
The bus had seating for 68, or had 68 persons in it.
The total time was 1.7 hours.
And the one infected person managed
to infect around 21 others, when we account
for some that may have been infected at the event, given
the low rate of infection to people outside of the bus.
Using those numbers and taking into
account the size of the bus and the fact
that there was no forced ventilation--
this was a winter ride.
And there was only natural ventilation--
and if we use a value that's been measured
for other types of public transit buses
where no forced ventilation is occurring,
then we conclude that the Cq for this event
is around 72 quanta per meter cubed, which
is a very consistent estimate with what we obtained before
for a situation where people are perhaps speaking
in an intermediate tone on a noisy bus over that period
of time.
It's also important to note that a recent analysis
of the incident involving interviews
of all the people involved established that there
was no correlation between the position of a person
with respect to the infected person in the seating
chart of the bus relative to whether they got infected
or not.
So in other words, it was not short-range transmission
through puffs or respiratory jets.
But instead somehow, there was a circulation
throughout the bus of infected air as the most
plausible explanation.
Our third example is the Diamond Princess.
So this was the quarantined cruise ship
in Yokohama Port, Japan.
There were 3,011 passengers and crew onboard.
And the quarantine lasted for 12 days,
or around 288 hours, at which point people began to leave.
And we won't use any data from that point.
The quarantine is a good chance for us
to study airborne transmission, because people were largely
confined to their room.
So of course, some of the crew were going back and forth,
bringing food and checking on the passengers.
But the vast majority of people were essentially
cooped up in their room with their fellow travelers
or family members in small groups,
typically with the windows closed because this
was in the winter, and with ventilation
which was doing a significant amount of recirculation
between the rooms.
And in fact, transmission occurred
across different rooms, where people
did not have direct contact with a known infected person
and yet still managed to get infected.
In those 12 days, the number of infections grew very rapidly
and, in fact, had sort of an exponential increase.
So in the end, there were 354 infected persons
when they began releasing passengers after 12 days.
And the fact that the shape of the infections versus time is
an increasing exponential-like curve suggests that this cannot
be modeled by the Wells-Riley equation, where instead,
the number of infected people has to saturate as you run out
of susceptibles.
So this acceleration of the number
of infected people with time is best attributed to incubation.
And it is known that the incubation time for COVID-19
is around 5.5 days.
Some people may have been infected,
and likely were infected, before the start of the quarantine.
So there definitely were infected people
generating newly infectious people during the time
of the quarantine.
So as a simple analysis of this incident, we can use--
or let us use--
our model for fast incubation.
We have an analytical solution for the trend in the number
of cases versus time.
And as you can see in the figure,
this model has a pretty good fit to the growth
in the number of cases.
And if we fit that model and infer what is the value of Cq,
then we come out with a number around 30 quanta
per meter cubed, again, very consistent with all
the other inferences and basically consistent with light
activity, light normal speech, and sort of resting breathing
that was going on in the ship.
Now, there definitely could be some debate over the way
that we've just analyzed the ship, in the sense that we
had analyzed it from the perspective
of a well-mixed ship.
So we're assuming that the infectious aerosols were spread
throughout the ship uniformly.
So that is obviously a gross estimate, very crude.
On the other hand, we get a very reasonable result.
And there is evidence that transmission was occurring
through the vents, through the hallways, and through the air
to large numbers of people.
And so the fact that we get a reasonably consistent number
of 30 quanta per meter cubed compared
to all of our other estimates does
support the idea of airborne transmission occurring
in a somewhat uniform and well-mixed fashion
across the ship.
Yet another inference we could make
would be to look at the initial spreading
of the epidemic in Wuhan, China, where it first originated.
So there have been a number of studies
of the initial spreading.
And the reproductive number of the spreading
of the disease, R0, has been estimated to be around 3.5.
In fact, there's a range of estimates
from that time period, given the sort of somewhat limited data.
But that's the agreed upon average number.
Now, there is an interesting thought exercise
we can do looking at that number if we make the assumption
that the majority of transmissions
occurred indoors, in people's family homes or apartments.
So if we take the time period for the spreading
of the infection in our analysis to be 5.5 days, which
is the average incubation time, and we
use the average size of a Chinese household
in that region of 3.03 people, and we
assume an average size of a Chinese apartment for that size
family of 90 meters cubed, and we also
assume measured typical natural ventilation
rates for this time of winter of around 0.3 per hour,
or a 3-hour air change time roughly, then
interestingly enough, from that analysis,
we find Cq again is 30 quanta per meter
cubed, the same as the number that we
got for the Diamond Princess.
So again, this is a very crude estimate.
This analysis is even more crude than the analysis of the ship.
We're looking at the entire population of a city.
And we're assuming that the spreading is happening
in people's homes when they spend time together
for long periods of time, sharing indoor air which
is typically not very well ventilated,
and not wearing masks, importantly.
So at that time, people were absolutely
wearing masks outside the house.
And in fact, for much of that time,
people were confined to their apartments
even under threat of force from the authorities.
So people were definitely spending a lot of time
in their homes with their families.
And it's interesting to observe that despite that quarantine
that the spreading still occurred fairly rapidly.
And it occurred in a way which is
consistent with indoor transmission in people's homes.
So if we take all of this analysis
and come back to our figure of Cq values--
again, that's the number of infection quanta
per meter cubed of exhaled breath
for an infected individual--
then we can put our inferences for the Ningbo bus, the Diamond
Princess, and the Wuhan outbreak on the same plot
as the values we inferred by rescaling the value of 900
for the Skajit Valley Chorale.
And what we find, again, is a very consistent set
of estimates over a range of respiratory activities, which
tells us that the Cq is around on the order of 10 or so,
or tens, for light activity and resting breathing.
It's in the range of 10 to 100, or maybe several hundred,
for speech at different levels of volume,
which roughly-- the number of droplets
is known to increase roughly linearly with the decibel level
of speech.
And then singing has a more--
obviously a much, much greater release of
particles and aerosols.
And that's at a much higher level, in the many hundreds.
So I think those are fairly consistent numbers, which
again, looking at most of these cases, are conservative
and could be applied in the guideline
to a wide range of examples involving
other types of populations, which may be healthier,
younger, less likely to transmit,
compared to all of these super spreading incidents.