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PROFESSOR: So let's
go through, now,

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how we can parameterize
our guideline specifically

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for COVID-19 by looking at
specific superspreading events.

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So the event that was analyzed
in great detail first,

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and which is going to
be of most use for us

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initially for parameterizing
the guideline,

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is the Skajit Valley Chorale
superspreading incident.

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So this was, again, a 2
and 1/2 hour choir practice

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involving 61 people, one of
whom was known to be infected.

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The practice lasted
2 and 1/2 hours.

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And in the end, there were 53
infected people, two of whom

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later died.

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So this was a large room with
a height of 4 and 1/2 meters

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and an area of 180
meters squared.

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It was poorly ventilated.

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The heat was on for a
certain amount of time

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and then taken off.

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And the average air change rate
was estimated at 0.65 per hour.

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And of course, the people were
singing for much of the time,

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leading to much higher
rates of droplet emission.

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And in fact, I think we can
assume for this event, given

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the huge number
of infections that

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occurred in such a short
time, that the index patient--

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the index case-- was at
near the peak viral load,

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peak of infection.

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And also, that allows us to
make a conservative estimate

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of using that for
calibrating our guideline.

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So if we look at
the figure here,

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we can see the
droplet distributions

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taken from experimental
measurements

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of Morawska et al in 2009.

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And those droplet distributions
have been fed into the model

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that we just described
and evolved in time

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in such a way that corresponds
to the conditions of the Skajit

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Valley Choir itself.

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And so what we can see is
that the droplet distribution

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corresponding to singing--

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or the closest
approximation of singing,

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which are measurements
of voiced aahs

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from the original experiment--

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that distribution is much
bigger than all the others.

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It has a very broad tail
to somewhat larger sizes.

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But it has a peak
just below 1 micron.

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Similarly, the other
types of activities

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measured in the
original study, which

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correspond to, for example,
whispered ahh or speaking

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or in counting of
numbers, for example,

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or various forms of breathing
through the nose and the mouth

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or only through the nose--

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all those distributions have
much lower sort of magnitude

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or number of drops.

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And this is also drop volume.

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We have accounted for the
size of the drops as well.

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So it's the total droplet volume
per total volume or volume

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fraction.

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And the peak of all
the distributions

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is in a similar place,
just below 1 micron,

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so again, corresponding
to the aerosol range.

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And it's important that we take
those droplet distributions

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and evolve them in the
Skajit Valley Choir space.

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So then, we can figure out
which of those droplets

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survived and would be in the air
and would be then corresponding

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to the airborne
transmission and can

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be compared with the actual
spreading events that occurred

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using the Wells-Riley model.

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So is it a short amount of time?

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We're going to assume there was
no delay caused by incubation.

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But rather, people were getting
infected but not passing it

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on to anybody else.

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And so we will use
the Wells-Riley model.

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So when we do that
fitting, we come out

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with a value of Cq, the number
of infection quanta per volume

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in the exhaled breath
of the infected person,

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around 900 quanta
per meter cubed.

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A published study
of Miller et al

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came to a similar conclusion
of 870 quanta per meters cubed.

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And so we can take that to be
a reasonable value for singing.

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Now, if we go to
the next figure,

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we can include all of these
estimated total quanta

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concentrations corresponding
to different hypothetical forms

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of respiration in the
Skajit Valley Choir

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and use that for rescaling.

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So we can say, the choir was
actually involving singing.

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And that gave us a
number around 900.

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And then if we rescale,
the other amounts

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of respiratory
droplets corresponding

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to different activities would
have correspondingly scaled

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values of Cq.

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And as a further calibration,
we can compare it

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with another recent study
of Asadi and Ristenpart,

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where again, different types
of respiratory activities

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were measured for their
aerosol size distributions,

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including speaking at
different levels of volume

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and also breathing
in different ways.

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And if we line up
two values that

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correspond to sort of
intermediate speech

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as a calibration, then
we find that the quanta

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values that we infer--

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the Cq values-- for both of
those independent studies

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of respiratory droplets
really correlate nicely

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across different
types of activities

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from breathing to
speaking to singing,

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allowing us a consistent
definition of Cq,

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again, for a situation
corresponding

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to most likely peak infectivity.

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So we are talking about
sort of the worst case

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scenario in order to derive
a conservative guideline.

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It should also be noted that the
median age of the choir members

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was 69.

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And by using this
spreading incident,

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we are again being conservative,
because it is well established

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that elderly persons have an
elevated risk of complications

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and even death from
COVID-19, and perhaps also

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some evidence showing
increased risk of transmission.

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So therefore, when we
apply the guideline

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to a general
population, including

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younger and healthy
people, that we

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will find that we are making
a conservative estimate,

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which is our goal.

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So at this point, we have a
fully parameterized guideline.

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And we have consistent
values of Cq

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across a range of
respiratory activities

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involving two different studies
of respiratory aerosols,

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all coming from the
Skajit Choir incident.

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So now, let's look at some
other spreading incidents

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to see if we can get
consistent values of Cq

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in cases where people
were not singing

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and where the size of
the room was different,

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and sort of see
if we really have

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a transferable inference here.

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And if we do find
consistent numbers,

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it provides further
evidence to support

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the hypothesis of
airborne transmission

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in all of these cases.

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So the next example
we'll look at

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is the incident of the Tiantong
Temple religious ceremony

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and, in particular, the buses
that went back and forth

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from that ceremony.

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One bus, in particular, was
similar to this Dongfeng tour

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bus luxury liner,
which underwent

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a 100-minute trip to Ningbo and
then back in the same seating.

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The bus had seating for 68,
or had 68 persons in it.

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The total time was 1.7 hours.

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And the one infected
person managed

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to infect around 21
others, when we account

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for some that may have been
infected at the event, given

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the low rate of infection to
people outside of the bus.

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Using those numbers
and taking into

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account the size of
the bus and the fact

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that there was no
forced ventilation--

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this was a winter ride.

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And there was only
natural ventilation--

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and if we use a value
that's been measured

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for other types of
public transit buses

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where no forced
ventilation is occurring,

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then we conclude that
the Cq for this event

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is around 72 quanta
per meter cubed, which

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is a very consistent estimate
with what we obtained before

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for a situation where
people are perhaps speaking

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in an intermediate tone on
a noisy bus over that period

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of time.

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It's also important to
note that a recent analysis

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of the incident
involving interviews

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of all the people involved
established that there

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was no correlation between
the position of a person

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with respect to the infected
person in the seating

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chart of the bus relative
to whether they got infected

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or not.

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So in other words, it was
not short-range transmission

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through puffs or
respiratory jets.

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But instead somehow,
there was a circulation

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throughout the bus of
infected air as the most

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plausible explanation.

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Our third example is
the Diamond Princess.

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So this was the
quarantined cruise ship

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in Yokohama Port, Japan.

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There were 3,011 passengers
and crew onboard.

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And the quarantine
lasted for 12 days,

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or around 288 hours, at which
point people began to leave.

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And we won't use any
data from that point.

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The quarantine is a
good chance for us

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to study airborne transmission,
because people were largely

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confined to their room.

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So of course, some of the crew
were going back and forth,

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bringing food and checking
on the passengers.

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But the vast majority of
people were essentially

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cooped up in their room
with their fellow travelers

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or family members
in small groups,

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typically with the windows
closed because this

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was in the winter,
and with ventilation

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which was doing a significant
amount of recirculation

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between the rooms.

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And in fact,
transmission occurred

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across different
rooms, where people

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did not have direct contact
with a known infected person

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and yet still managed
to get infected.

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In those 12 days, the number
of infections grew very rapidly

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and, in fact, had sort of
an exponential increase.

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So in the end, there
were 354 infected persons

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when they began releasing
passengers after 12 days.

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And the fact that the shape of
the infections versus time is

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an increasing exponential-like
curve suggests that this cannot

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be modeled by the Wells-Riley
equation, where instead,

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the number of infected people
has to saturate as you run out

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of susceptibles.

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So this acceleration
of the number

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of infected people with time is
best attributed to incubation.

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And it is known that the
incubation time for COVID-19

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is around 5.5 days.

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Some people may
have been infected,

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and likely were infected, before
the start of the quarantine.

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So there definitely
were infected people

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generating newly infectious
people during the time

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of the quarantine.

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So as a simple analysis of
this incident, we can use--

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or let us use--

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our model for fast incubation.

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We have an analytical solution
for the trend in the number

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of cases versus time.

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And as you can
see in the figure,

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this model has a pretty
good fit to the growth

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in the number of cases.

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And if we fit that model and
infer what is the value of Cq,

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then we come out with a
number around 30 quanta

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per meter cubed, again,
very consistent with all

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the other inferences and
basically consistent with light

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activity, light normal speech,
and sort of resting breathing

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that was going on in the ship.

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Now, there definitely could
be some debate over the way

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that we've just analyzed the
ship, in the sense that we

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had analyzed it
from the perspective

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of a well-mixed ship.

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So we're assuming that the
infectious aerosols were spread

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throughout the ship uniformly.

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So that is obviously a
gross estimate, very crude.

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On the other hand, we get
a very reasonable result.

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And there is evidence that
transmission was occurring

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through the vents, through the
hallways, and through the air

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to large numbers of people.

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And so the fact that we get a
reasonably consistent number

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of 30 quanta per
meter cubed compared

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to all of our other
estimates does

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support the idea of airborne
transmission occurring

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in a somewhat uniform
and well-mixed fashion

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across the ship.

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Yet another inference
we could make

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00:13:02,270 --> 00:13:04,280
would be to look at
the initial spreading

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of the epidemic in Wuhan, China,
where it first originated.

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So there have been
a number of studies

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of the initial spreading.

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00:13:12,710 --> 00:13:15,500
And the reproductive
number of the spreading

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00:13:15,500 --> 00:13:20,160
of the disease, R0, has been
estimated to be around 3.5.

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00:13:20,160 --> 00:13:21,710
In fact, there's a
range of estimates

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00:13:21,710 --> 00:13:24,710
from that time period, given the
sort of somewhat limited data.

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00:13:24,710 --> 00:13:28,700
But that's the agreed
upon average number.

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00:13:28,700 --> 00:13:31,610
Now, there is an
interesting thought exercise

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00:13:31,610 --> 00:13:35,750
we can do looking at that
number if we make the assumption

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00:13:35,750 --> 00:13:38,000
that the majority
of transmissions

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00:13:38,000 --> 00:13:43,340
occurred indoors, in people's
family homes or apartments.

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00:13:43,340 --> 00:13:47,210
So if we take the time
period for the spreading

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00:13:47,210 --> 00:13:51,110
of the infection in our
analysis to be 5.5 days, which

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00:13:51,110 --> 00:13:53,240
is the average
incubation time, and we

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00:13:53,240 --> 00:13:56,480
use the average size
of a Chinese household

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00:13:56,480 --> 00:14:00,650
in that region of
3.03 people, and we

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00:14:00,650 --> 00:14:03,920
assume an average size of a
Chinese apartment for that size

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00:14:03,920 --> 00:14:07,010
family of 90 meters
cubed, and we also

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00:14:07,010 --> 00:14:10,910
assume measured typical
natural ventilation

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00:14:10,910 --> 00:14:17,020
rates for this time of winter
of around 0.3 per hour,

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00:14:17,020 --> 00:14:21,020
or a 3-hour air change
time roughly, then

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00:14:21,020 --> 00:14:23,900
interestingly enough,
from that analysis,

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00:14:23,900 --> 00:14:27,600
we find Cq again is
30 quanta per meter

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00:14:27,600 --> 00:14:29,150
cubed, the same as
the number that we

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00:14:29,150 --> 00:14:31,850
got for the Diamond Princess.

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00:14:31,850 --> 00:14:34,190
So again, this is a
very crude estimate.

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00:14:34,190 --> 00:14:37,130
This analysis is even more crude
than the analysis of the ship.

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00:14:37,130 --> 00:14:40,380
We're looking at the entire
population of a city.

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00:14:40,380 --> 00:14:42,470
And we're assuming that
the spreading is happening

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00:14:42,470 --> 00:14:44,750
in people's homes when
they spend time together

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00:14:44,750 --> 00:14:47,840
for long periods of time,
sharing indoor air which

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00:14:47,840 --> 00:14:50,720
is typically not
very well ventilated,

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00:14:50,720 --> 00:14:52,700
and not wearing
masks, importantly.

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00:14:52,700 --> 00:14:55,820
So at that time,
people were absolutely

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00:14:55,820 --> 00:14:57,190
wearing masks outside the house.

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00:14:57,190 --> 00:14:58,650
And in fact, for
much of that time,

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00:14:58,650 --> 00:15:01,470
people were confined
to their apartments

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00:15:01,470 --> 00:15:03,470
even under threat of force
from the authorities.

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00:15:03,470 --> 00:15:05,990
So people were definitely
spending a lot of time

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00:15:05,990 --> 00:15:07,760
in their homes with
their families.

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00:15:07,760 --> 00:15:11,060
And it's interesting to observe
that despite that quarantine

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00:15:11,060 --> 00:15:13,850
that the spreading still
occurred fairly rapidly.

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00:15:13,850 --> 00:15:15,230
And it occurred
in a way which is

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00:15:15,230 --> 00:15:19,640
consistent with indoor
transmission in people's homes.

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00:15:19,640 --> 00:15:21,590
So if we take all
of this analysis

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00:15:21,590 --> 00:15:25,520
and come back to our
figure of Cq values--

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00:15:25,520 --> 00:15:28,790
again, that's the number
of infection quanta

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00:15:28,790 --> 00:15:30,620
per meter cubed
of exhaled breath

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00:15:30,620 --> 00:15:32,630
for an infected individual--

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00:15:32,630 --> 00:15:36,620
then we can put our inferences
for the Ningbo bus, the Diamond

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00:15:36,620 --> 00:15:39,410
Princess, and the Wuhan
outbreak on the same plot

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00:15:39,410 --> 00:15:45,590
as the values we inferred by
rescaling the value of 900

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00:15:45,590 --> 00:15:48,500
for the Skajit Valley Chorale.

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00:15:48,500 --> 00:15:50,780
And what we find, again,
is a very consistent set

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00:15:50,780 --> 00:15:54,440
of estimates over a range of
respiratory activities, which

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00:15:54,440 --> 00:16:01,790
tells us that the Cq is around
on the order of 10 or so,

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00:16:01,790 --> 00:16:06,020
or tens, for light activity
and resting breathing.

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00:16:06,020 --> 00:16:09,250
It's in the range of 10 to
100, or maybe several hundred,

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00:16:09,250 --> 00:16:11,900
for speech at different
levels of volume,

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00:16:11,900 --> 00:16:13,910
which roughly-- the
number of droplets

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00:16:13,910 --> 00:16:17,480
is known to increase roughly
linearly with the decibel level

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00:16:17,480 --> 00:16:18,470
of speech.

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00:16:18,470 --> 00:16:21,620
And then singing has a more--

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00:16:21,620 --> 00:16:24,950
obviously a much, much
greater release of

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00:16:24,950 --> 00:16:26,870
particles and aerosols.

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00:16:26,870 --> 00:16:30,770
And that's at a much higher
level, in the many hundreds.

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00:16:30,770 --> 00:16:34,790
So I think those are fairly
consistent numbers, which

316
00:16:34,790 --> 00:16:38,210
again, looking at most of
these cases, are conservative

317
00:16:38,210 --> 00:16:40,460
and could be applied
in the guideline

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00:16:40,460 --> 00:16:43,970
to a wide range of
examples involving

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00:16:43,970 --> 00:16:46,790
other types of populations,
which may be healthier,

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00:16:46,790 --> 00:16:49,460
younger, less
likely to transmit,

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00:16:49,460 --> 00:16:53,440
compared to all of these
super spreading incidents.