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PROFESSOR: So now
let's summarize

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where we've come to in our
analysis of short-range effects

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from respiratory jets
relative to long range

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airborne transmission which
we previously calculated.

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And let's also
think about what are

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the implications for policy.

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And for personal decisions about
safety during the pandemic.

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So first of all,
when masks are worn,

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we've already discussed the
filtering effect of masks.

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We've talked about
how that brings

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a squared factor of the
mask penetration factor

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which leads to a very
substantial increase

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in the reduction in
the transmission rate.

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But there's another
important factor

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when you have a mask, even a
fairly poor mask, a cloth mask,

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it may not be so great a
blocking aerosol particles

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but it's very good
at blocking momentum

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so the fluid momentum that
comes from just normal breathing

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is almost completely
stopped by a mask.

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Even a vigorous cough only
lets some momentum through

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and a few droplets from
more violent activities

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such as that.

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So what's more typical in a case
where people are wearing masks

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is that there is sort of
some exhaled air slowly

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building up around you without
very much additional momentum.

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And as we've discussed that air
is warmer and tends to rise.

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And so typically
the thermal plume

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of kind of the exhaled
air rising above you a bit

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like a chimney and that's where
the droplets initially reside.

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We're not likely to directly
infect anybody by that method,

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either because people
aren't close enough

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or they aren't above
the other person.

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And then, of course,
there are other flows

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in the room that
we've discussed,

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which are often turbulent.

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And those will transport
the droplets everywhere

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and will lead to
the well-mixed room

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as being the most
natural and most accurate

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first approximation
for the infection risk

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by another person who
is also wearing a mask.

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So I would argue that no
strict social distancing is

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required in a mask situation.

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So whether we're six
feet or three feet,

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it's not going to give us
substantially more safety

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if people are wearing masks.

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And instead we should pay much
more attention to the formula

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that I boxed here,
which gives you

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an estimate of the long range
transmission risks airborne

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which is equally there
for everyone in the room.

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And that must be
considered for safety

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and also for contact tracing.

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Now situation is very
different without masks.

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As we've seen without masks, we
are imparting a lot of momentum

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to the fluid, the air.

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Simply by breathing
and certainly

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by talking or singing
or exercising,

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we're really pushing the
air around and launching

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those particles into the air.

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And even at three
feet or six feet

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there can be still
a substantial risk.

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Although as we
said, the difference

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between three and
six is not so great.

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So one might consider
switching to three.

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On the other, hand,
even six may not

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be enough protection you
might need to be thinking

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about longer distancing.

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And of course, there is
always the airborne risk.

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So at some point, you
hit that point x_c

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where the airborne risk is
comparable to the short-range

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risk.

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And also there are people such
as the guy I sketched back here

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which are not in
the respiratory jet

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and probably have a lower
risk than the average.

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So it's definitely
important to still consider

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the average risk coming from
the long range guideline.

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But one could add a correction
to be very conservative

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for cases such as sketched
here when this poor person is

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finding himself or herself
in the respiratory jet

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for long periods of time.

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So let's imagine there's a
typical spacing, x bar, which

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would be sort of the
worst case but still

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typical spacing one might expect
of the people in the rooms.

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If you think there's a
certain situation where

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maybe two of the people might
be five feet apart or four,

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three feet apart and
facing each other

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for sniffing amounts
of time, and then p jet

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is the probability that
they are encountering

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each other's respiratory jets.

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Or maybe put another
way, the fraction

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of the time one person
spends in another person's

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respiratory jet.

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When that happens
the transmission

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is just between two people.

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It's not to the entire room.

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So that's another very important
factor to keep in mind,

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this factor of n, the
occupancy, doesn't really

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come up in the social
distancing model

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here when we're talking about
the indoor reproductive number.

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So to make a modified
guideline, we

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can take the long range
indoor reproductive number

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and add a short
range correction.

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We've already calculated
what this looks like.

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So if I write the
guideline as n minus 1 tau

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is less than epsilon
over the average beta,

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I can also restore
what that means here.

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Average beta times tau is the
integral, time interval data,

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basically, of the
transmission rate.

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And so this fact
that we've already

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calculated the ratio
of the shortrange term

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to the longer term
is x_c over x--

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or x bar times p jet.

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It's a very simple correction.

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If we plug back in our estimates
for this average beta then

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we arrive at this formula here.

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The first term is the same
guideline we already have.

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And there's a new term
now which, notice,

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does not involve n and
doesn't have the mass factor,

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of course, as well.

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But it involves the length,
so social distancing.

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And it involves the mouth
area and the breathing rate.

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The breathing rate
now is also not

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coming in square
because we're assuming

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that the breath is already
providing this concentration.

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And we're just looking at
another distance downstream.

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And the Qb is for the receiving
person's inhaling breath rate

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whereas the QB squared comes
from inhaling and exhaling

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and finding the steady
state in the room.

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And so we've already
estimated how big

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this term is [? xc ?]
over x might be anywhere

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from one to 100 or maybe even
1,000 if you let p jet be 1.

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So if you stand facing
another person continuously,

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this can be a large term and
can actually dominate the other.

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I'll notice there's an n there.

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So still, there
could be a balance.

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But when you take into account
that people are not always

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directly facing
each other so much,

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then this number might
be a lot smaller.

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And I would argue
that in many cases

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the dominant term is
the long range one.

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And the short range
one is the correction.

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But one should be
aware of situations

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where the short-range
effect could be dominant.

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And so that must
also be considered.

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And this modified guideline
here would be one way

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to take that into account.