WEBVTT

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PROFESSOR: So this
brings us to the conclusion

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of our Massive Open Online
Course, 10.S9,5 Physics

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of COVID-19 Transmission.

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So let's briefly review
what we've learned.

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We began by talking about
respiratory pathogens,

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both bacteria and viruses.

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And, in particular,
we focused on viruses

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and understood how
they can be transmitted

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through aerosol particles
through infected indoor air.

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And this includes the
important case of SARS-CoV-2,

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the virus that causes COVID-19.

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We then went on to use
epidemiological models

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and fluid-mechanical
analysis of a well-mixed room

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to arrive at a universal
indoor safety guideline

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to limit transmission
of the disease.

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A very important
conclusion is that it's not

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possible to bound
a single variable,

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as in all of the current
safety guidelines

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from various official
organizations.

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So, for example, you cannot
only bound the distance between

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people, for example,
6 feet, 1 meter.

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You cannot bound only the
occupancy, say, 25 persons.

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You can't even bound the
ventilation rate, say,

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a minimum of 15 cubic feet
per minute per person.

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Or you can't bound
only the time--

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let's say 15 minutes
or one hour--

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because all of these variables
are, inevitably, linked.

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And the simplest way to see that
is through our universal safety

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guideline, which
shows you how to limit

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the cumulative exposure time,
(N-1)t, which

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is a product of the
number of susceptible

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people in a room times
the time they're together

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with an infected person.

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And there are a number
of factors that come in.

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So epsilon is a
tolerance you can choose.

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And then there are these factors
lambda_V over --

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Q_b^2 P_m^2 Cq.

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And we can discuss, based on
that formula and our analysis

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throughout this course,
the most important ways

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of mitigating transition
based on this formula.

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So I've, roughly, put
them in order here.

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So the first thing is to wear
masks and, in particular,

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try to wear good masks.

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So these might be
surgical masks, N95s,

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but even various cloth
or silk masks, especially

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double-layer fabrics,
can be quite effective

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because, as P_m goes to 0,
the mask penetration factor,

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you can see this bound
gets larger and larger,

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like P_m^2.

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So a factor of 10%
transmission can still

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give you a factor of 100
compared to not wearing

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masks in terms of filtration.

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That's a very
significant amount.

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Secondly, we can
improve ventilation.

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And this can be by imposing
faster mechanical ventilation

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with more fresh air coming in.

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It could also be by opening a
window and turning on a fan.

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And that's increasing lambda_a.

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We can also try to spend more
time in larger rooms or even

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outside, which is,
basically, increasing V

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and, thereby, diluting
the air that is present

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and all the infectious aerosols.

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We can also look at
imposing air filtration.

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We've shown that there
is some benefit there.

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Although, it might not
be as large as you think.

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Even very good air
filtration doesn't

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buy you many orders of
magnitude because it's only

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filtering some of the
air, but not all of it,

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compared to masks, which
are filtering at the source

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and at the target and, thereby,
are much more effective.

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We can also try to make sure the
occupants of the room maintain

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lower activity
levels if possible.

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So they're breathing
less heavily.

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So they're exchanging air with
the space and with other people

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less frequently and
at a lower rate.

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We can also try to avoid
vocal exertions, which

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tend to lead to much larger
emissions of droplets,

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for example, singing being
a particularly bad case,

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but even loud voices can be a
lot worse than quiet voices.

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So, generally, keeping the
noise in the room down--

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I know this will be welcome
news for many teachers--

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but, in general,
that is a good way

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to try to limit transmission
to keep people calm.

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We can also take measures
to try to enhance

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the deactivation, the
natural elimination

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of the infectiousness
of the virus.

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One way to do that
is to maintain

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an intermediate, comfortable
range of humidity

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from 50% to 80%.

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So very dry air turns
out to be worse,

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and that is one of the reasons
that viral diseases tend

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to be seasonal, like the
seasonal flu, typically,

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worse in winter, in addition
to the fact that you're

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spending more time indoors.

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There's also ultraviolet
treatments that might be used,

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which is, effectively, like
another form of filtration.

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And then, finally,
we spent a lot

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of time talking about the fluid
mechanics of indoor spaces

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and of human respiration
and movement,

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and those considerations take
us beyond the well-mixed room.

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And the main thing
to remember there

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is, thinking back to our example
of people who are smoking,

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if someone is exhaling right
after breathing in a cigarette,

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there's sort of a narrow plume
of turbulent, very smoky air,

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which you want to avoid.

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And the same thing
is true when dealing

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with a respiratory
pathogen. You don't

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want to spend a lot of time in
the respiratory jet of a person

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who is not wearing a mask if
you don't know if they are sick,

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potentially, even asymptomatic.

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So that's an important just
general piece of advice,

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and we've given some insight
into how to quantify that.

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Although, any treatment of
short-range transmission

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through respiratory
jets is, inevitably,

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dependent upon assumptions
about the activity of the room.

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How much are you
turning your head?

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Where are people placed?

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And so, hence, you can't really
get a universal guideline,

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as opposed to this boxed
formula, which is, essentially,

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the mass balance
for the whole room.

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And that is a
universal guideline.

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We've also talked a bit
about types of ventilation.

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And, as opposed to ventilation
that seeks to mix the space,

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there may be situations
where having high ceilings

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and trying to take advantage of
buoyancy-driven thermal flows

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that you can sort of target the
airborne aerosols to be sitting

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higher in a room where
they could then be removed

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by ventilation at the top, which
is displacement ventilation.

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That's another strategy
that may be useful.

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So these are all different
strategies one can use.

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And which one is most
effective or makes

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the most sense in a given space
really depends on the details.

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And, in order to facilitate the
application of the guideline,

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we have provided an
online app and, also,

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a spreadsheet, which you
can use to adapt this

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to your own space.

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And I hope that you will
find the principles you've

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learned in this class
useful and that,

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perhaps, even you'll
find these tools useful,

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specifically, to combat the
transmission of COVID-19

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and, in the future, other
respiratory diseases.