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00:00:10,500 --> 00:00:13,960
PROFESSOR: So when we start
considering short-range effects

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of respiratory
jets and plumes, it

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00:00:16,750 --> 00:00:18,580
raises the interesting
question of what

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is the role of social
distancing, which

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is our primary
means for fighting

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00:00:22,480 --> 00:00:24,940
the pandemic at the moment.

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So as we've discussed, this
is especially important

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when masks or face
shields are not worn,

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so that the jets and plumes
that come from breathing

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and speaking and singing and
other respiratory activities

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are not blocked, in the sense
that the momentum is not

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blocked.

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And furthermore, there's
no filtering going on.

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So then we have our
long-range airborne risk

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coming from respiratory
aerosols that have become well

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mixed into the background air.

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But we have a new
term that comes

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from short-range transmission.

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And in a worst case
scenario, we can imagine that

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as a wedge-like or
cone-like plume,

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which we have just described.

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In reality, there is going
to be some background

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flows in the room,
which will sweep

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that jet in different
directions and break it up.

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There'll be motion of
people, turning of heads.

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So it'll never be this simple.

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But the worst case
scenario is really

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a well-formed respiratory
jet and somebody

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essentially standing right in
it at a certain distance, X bar,

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which is our sort of
average social distance.

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As we've discussed, we can also
take the ratio of these two

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terms and speak of fs,
which we define here

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as the short-range risk
enhancement factor.

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So that comes down
to two new parameters

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which we've been discussing--

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P jet, the probability
that a susceptible person

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is in the respiratory jet
of an infected person,

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and X bar, the typical distance
over which that occurs.

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Xc is this transition distance,
where the respiratory jet

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concentration starts to match
that of the background ambient

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air, which we substitute and
form this expression shown

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here.

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So there are a
number of situations

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we can think of to estimate
what would be these parameters.

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So the first would be just
to consider random occupant

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placement.

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So in this situation, if we view
from above, we have, let's say,

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a person.

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This is now viewing from above.

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And they have a respiratory
jet, which is going off

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like this in one direction.

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And then at any
given distance, we

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can imagine there's sort of a
typical social distance here.

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Now, I'm kind of exaggerating
how far that is compared

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to the size of the head.

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But if this distance here is
X bar, then at that distance,

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we'd like to say, what
is the probability

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that the susceptible
person is in the jet?

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And that would simply
be formed by taking

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the angle of the jet
relative to the full circle.

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So we could imagine,
what is the probability

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of putting a person right here
versus over here or over here

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where they're not
going to be in the jet?

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So in that situation,
we could write

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that P jet is approximately
the inverse tangent of alpha.

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So alpha, remember,
is the ratio--

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is the entrainment factor.

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And it's sort of the slope of
this line defining the cone

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of the respiratory jet.

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And then we can
divide that by pi.

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So that basically tells
us the probability

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of being in this yellow
region versus somewhere

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else at a given distance.

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And then, now, if we think
about the distance factor--

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if it's completely
random, then if we just

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imagine lots of people
scattered throughout a room--

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imagine a busy
space, for example,

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in a bar or a nightclub, a place
where it's somewhat crowded

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but people are kind
of moving around.

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Then we might have an average
social distance, which

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is the area of the
room divided by N.

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So that's the area per person.

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And then take a square root.

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That's an estimate
of the distance.

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And the square root of area
is the length L of the room.

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So it's divided by
square root of N.

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And so with these
two assumptions,

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we would then find that this
short-range risk enhancement

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factor--

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well, what does it look like?

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It then is this factor P
jet times Xc over L times--

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and then we have this
N minus 1 factor.

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So if N is larger than 1,
we could just estimate that

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as a square root of N. So what
that shows is as more and more

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people pack into the
room, we have an increase

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in the importance of long-range
versus short-range transmission.

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And this pre-factor here is
something which typically

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will be much less than 1,
because the probability

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of being in a jet-- if
alpha is around 0.1, 0.15,

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this turns out to be around 3%.

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OK, so that's-- it's not quite
as wide as I've sketched here.

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The jet is a little
bit more narrow.

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And we've already discussed
that Xc-- the distance where

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the concentration
in the jet starts

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to match that of the
ambient-- it does

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depend on the
conditions of the room

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and the ventilation
and other factors.

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But roughly speaking,
Xc is typically smaller

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than the size of the room.

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And so this factor here is
quite a bit less than 1.

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So you see that in
a random situation,

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the short-range transmission
starts to become important only

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when the number of
people becomes large.

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And it grows like
square root of N.

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And there's a certain point,
which might be at N equals 20

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or N equals 50 or N
equals 100, depending

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on the space, where
the short-range risk is

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larger than the risk
of the background

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airborne transmission.

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And that's, again, just
coming from random placement.

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So on the other hand, the
random placement situation

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is not quite the
best case scenario.

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But it's sort of a fairly
optimistic scenario.

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The best case scenario
is if people are always

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kind of having their
backs to each other,

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never breathing on each other.

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That never really happens.

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In fact, it's more typical in
human interactions for people

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to face each other.

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They may be talking to each
other, looking at each other.

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And so hence, we tend to
find ourselves more typically

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in the way of breathing.

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And so it might be better
to think about this estimate

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in other ways.

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So a second way
that we can think

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about it is by using
a social distance

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guideline, or a social
distancing rule, let's

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just say.

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So let's say that instead
of a random situation

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where people are keeping
sort of the average distance

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between each other,
that no matter

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how many people in the room up
to a certain maximum occupancy,

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they're not going to
come within, let's

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say, a 6-foot radius or a
3-foot radius, 1-meter radius.

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Depending on what the
social distancing guideline

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is in that region,
there's going to be

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a certain sort of minimum X.

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And let's just think of that
as the worst case scenario.

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For the people that are that
close to each other, that's

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the distance we'll choose.

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And so this might be something
like 6 feet, 1 meter.

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You can pick.

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And in that case, the
fs is P jet over N

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minus 1 times Xc over
X. And we've already

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estimated that at
6 feet, Xc over X,

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it does depend on the
ventilation and the size

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of the room and other factors.

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But we've already said
that this factor here

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might be something like 6 to 600
for a certain set of examples

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that we've just considered.

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So when we put
all this together,

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if we take into account
also that P jet is around,

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let's say, 3%--

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if we imagine having
random placement of people

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but at a fixed distance,
minimum distance, of 6 feet,

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then what we'll
find is this ends up

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being something like 0.2
over N ranging up to,

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let's say, 20 over N. And
again, this is just very rough.

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So this is with random angle.

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So in other words,
we're still thinking now

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of just this kind of random
orientation of somebody's head,

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not necessarily facing
one person all the time.

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And so you can see
here that if N is--

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if we're in the situation of
the 20, which is-- by the way,

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that's the case where
this is getting large.

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So that would be a
case of a large room.

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Or it would be of low
breathing rates, et cetera.

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Then we-- you can see
that when N gets--

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if N is small, then this number
can actually be quite large.

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So in other words, if we just
have a few people in the room,

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and they can get this
close to each other--

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like one minimum social
distance, like 6 feet--

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then the primary risk is coming
from airborne transmission,

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especially if the
room is very big.

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If two people are by
themselves in an enormous room,

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then the risk from background
airborne transmission

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is minimal compared to the
risk of direct short-range

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transmission.

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So that kind of
makes sense, right?

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On the other hand,
notice the effect of N.

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If you have more and
more people in the room,

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00:09:36,970 --> 00:09:39,520
then even though most of those
people are a lot farther away,

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there's so many of them
that are potentially

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going to get infected
that it becomes worse,

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even in the case
of 20 here, which

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is sort of the more conser--

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00:09:48,860 --> 00:09:51,440
the case where short-range
is more important.

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00:09:51,440 --> 00:09:55,720
It starts to switch to where the
long-range transmission becomes

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00:09:55,720 --> 00:09:57,400
more important when
N is larger than 20

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00:09:57,400 --> 00:09:58,610
in this particular example.

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00:09:58,610 --> 00:10:07,310
So basically, so
significant for small N

202
00:10:07,310 --> 00:10:12,320
and basically large V. So
basically, low-occupant

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00:10:12,320 --> 00:10:14,700
densities-- if people are
to come close to each other,

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00:10:14,700 --> 00:10:16,570
then it makes sense
short-range is important.

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00:10:16,570 --> 00:10:18,680
In fact, a limit that we
haven't talked about yet

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00:10:18,680 --> 00:10:19,910
is, what if we're outside?

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00:10:19,910 --> 00:10:21,290
What if we don't
even have-- what

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00:10:21,290 --> 00:10:24,060
if the V goes to infinity
or V is very large,

209
00:10:24,060 --> 00:10:25,490
so effectively it's infinity?

210
00:10:25,490 --> 00:10:27,020
What this is telling
us is that we

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00:10:27,020 --> 00:10:29,720
have to stop worrying about
the long-range background

212
00:10:29,720 --> 00:10:32,320
well-mixed concentration
of infectious aerosols.

213
00:10:32,320 --> 00:10:34,370
And instead, we have to
focus on the short range.

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00:10:34,370 --> 00:10:36,210
Just whenever people are
coming close to each other,

215
00:10:36,210 --> 00:10:37,870
make sure they're not
breathing directly

216
00:10:37,870 --> 00:10:39,780
on each other for
long periods of time.

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00:10:39,780 --> 00:10:40,790
That's the key.

218
00:10:40,790 --> 00:10:42,290
Now, the last thing
we can think of,

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00:10:42,290 --> 00:10:45,000
which is really kind of
like a worst case scenario--

220
00:10:48,860 --> 00:10:52,250
that would be where a person is
at the closest distance that's

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00:10:52,250 --> 00:10:53,990
allowed or expected--

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00:10:53,990 --> 00:10:57,200
let's say, 6 feet, maybe
even 3 feet, 1 meter.

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00:10:57,200 --> 00:10:59,630
And also, they're not
randomly placed and angled.

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00:10:59,630 --> 00:11:01,340
But they're really
just constantly

225
00:11:01,340 --> 00:11:03,300
in the jet of the other person.

226
00:11:03,300 --> 00:11:07,100
So let's say, for
example, P jet is 90%.

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00:11:07,100 --> 00:11:09,290
That's a pretty high
number, keeping in mind

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00:11:09,290 --> 00:11:12,480
that there's also turbulent
and chaotic flows in the room,

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00:11:12,480 --> 00:11:15,140
such that even if you're
facing somebody all the time,

230
00:11:15,140 --> 00:11:18,020
the stable respiratory
jet and puff

231
00:11:18,020 --> 00:11:20,640
train is going to be swept
away by other currents.

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00:11:20,640 --> 00:11:23,270
And so it's really not as though
the other person is constantly

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00:11:23,270 --> 00:11:24,530
going to be in--

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00:11:24,530 --> 00:11:25,280
fully exposed.

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00:11:25,280 --> 00:11:27,830
But let's just say, we pick a
number like 90%, which is kind

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00:11:27,830 --> 00:11:29,850
of like a worst case scenario.

237
00:11:29,850 --> 00:11:32,270
And we're always
facing each other.

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00:11:32,270 --> 00:11:33,710
So let's, again, pick--

239
00:11:33,710 --> 00:11:36,410
X bar is, let's
just say, 6 feet.

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00:11:36,410 --> 00:11:38,540
Let's just say,
maybe we're sitting

241
00:11:38,540 --> 00:11:41,540
across a table at
a distance which

242
00:11:41,540 --> 00:11:43,280
is sort of an acceptable
social distance

243
00:11:43,280 --> 00:11:46,130
according to the 6-foot rule.

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00:11:46,130 --> 00:11:49,640
Then we're going to find that
this enhancement factor is

245
00:11:49,640 --> 00:11:56,900
around 6 over N to
600 over N. So we

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00:11:56,900 --> 00:12:05,720
can see that the short-range
effect can be a lot larger.

247
00:12:05,720 --> 00:12:07,770
So notice, even if N
gets to be really large,

248
00:12:07,770 --> 00:12:09,650
like a lot of people in
the room-- let's say,

249
00:12:09,650 --> 00:12:12,200
it's a restaurant with
100 people in the room--

250
00:12:12,200 --> 00:12:15,230
still, it's 6 times worse
to be in a single person's

251
00:12:15,230 --> 00:12:19,590
respiratory jet 90% of the
time at 6-foot distance.

252
00:12:19,590 --> 00:12:21,570
So that's actually
fairly alarming

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00:12:21,570 --> 00:12:26,360
if you think about situations
such as restaurants or office

254
00:12:26,360 --> 00:12:28,450
meetings or any
other normal activity

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00:12:28,450 --> 00:12:29,870
where people are
facing each other

256
00:12:29,870 --> 00:12:33,230
and breathing on each
other continuously

257
00:12:33,230 --> 00:12:35,420
without wearing masks
or face shields.

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00:12:35,420 --> 00:12:36,570
So this would be--

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00:12:36,570 --> 00:12:40,560
I'll just mention
here, short-range

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00:12:40,560 --> 00:12:45,900
dominates in this situation.

261
00:12:45,900 --> 00:12:48,050
So then, how do we
mitigate against

262
00:12:48,050 --> 00:12:50,000
this short-range
transmission risk, which

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00:12:50,000 --> 00:12:53,120
is going to be worse, again,
when we have people that

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00:12:53,120 --> 00:12:54,830
are not wearing
masks or face shields

265
00:12:54,830 --> 00:12:57,440
and are in close
proximity and facing

266
00:12:57,440 --> 00:12:59,890
each other for long
periods of time,

267
00:12:59,890 --> 00:13:03,050
and especially in a larger room
and a lower occupant density

268
00:13:03,050 --> 00:13:05,540
where the N is maybe
not so big, and we

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00:13:05,540 --> 00:13:08,150
don't have to worry as much
about long-range transmission?

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00:13:08,150 --> 00:13:10,800
Well, one way to
proceed is to continue

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00:13:10,800 --> 00:13:12,470
using the universal
guideline that we've

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00:13:12,470 --> 00:13:14,150
derived right here
for long range,

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00:13:14,150 --> 00:13:18,630
and simply choose a small
epsilon, much less than 1.

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00:13:18,630 --> 00:13:20,880
And you can see here, it
doesn't have to be that tiny.

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00:13:20,880 --> 00:13:26,220
From this simple estimate
here, maybe an epsilon of 0.01

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00:13:26,220 --> 00:13:29,130
might not be so bad because,
see, this number 600 is there.

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00:13:29,130 --> 00:13:32,010
And if N is maybe 5
or 10 in the room,

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00:13:32,010 --> 00:13:33,940
then that might be
already helping you.

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00:13:33,940 --> 00:13:36,900
So remember, we use the
guideline with a fudge factor,

280
00:13:36,900 --> 00:13:38,760
or a tolerance, epsilon.

281
00:13:38,760 --> 00:13:41,560
And some of the uncertainties in
different modes of transmission

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00:13:41,560 --> 00:13:44,120
are already kind of
included in there.

283
00:13:44,120 --> 00:13:45,870
But certainly, if we're
not wearing masks,

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00:13:45,870 --> 00:13:47,410
the risk is pretty high.

285
00:13:47,410 --> 00:13:49,150
And so that may not be enough.

286
00:13:49,150 --> 00:13:54,760
And that's why social
distancing can help.

287
00:13:54,760 --> 00:13:56,800
But I want to emphasize
from our discussion

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00:13:56,800 --> 00:13:58,960
of these respiratory
plumes, there's

289
00:13:58,960 --> 00:14:01,840
nothing really that
special about 6 feet.

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00:14:01,840 --> 00:14:05,460
There's unfortunately today a
feeling in the general public

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00:14:05,460 --> 00:14:06,880
that if you're
closer than 6 feet,

292
00:14:06,880 --> 00:14:08,130
you're at extremely high risk.

293
00:14:08,130 --> 00:14:09,670
You've penetrated
somebody's bubble.

294
00:14:09,670 --> 00:14:11,590
But when you're a little
bit more than 6 feet,

295
00:14:11,590 --> 00:14:13,340
you can breathe easy,
because you're safe.

296
00:14:13,340 --> 00:14:15,380
And you can see that's
really not true.

297
00:14:15,380 --> 00:14:18,280
If you are not wearing
masks, these respiratory jets

298
00:14:18,280 --> 00:14:20,410
and plumes can travel
very long distances.

299
00:14:20,410 --> 00:14:22,540
Of course, airborne
transmission is everywhere

300
00:14:22,540 --> 00:14:24,100
in the room at any distance.

301
00:14:24,100 --> 00:14:27,040
But even the elevated risk
of short-range transmission

302
00:14:27,040 --> 00:14:29,110
can extend further than 6 feet.

303
00:14:29,110 --> 00:14:31,570
On the other hand, when people
are turning their heads,

304
00:14:31,570 --> 00:14:33,970
and there's sort of
convection in the room

305
00:14:33,970 --> 00:14:37,000
and thermal convection as
we've been discussing, in fact,

306
00:14:37,000 --> 00:14:38,080
6 feet might be overkill.

307
00:14:38,080 --> 00:14:40,330
Maybe being even a little
bit closer might be OK.

308
00:14:40,330 --> 00:14:43,510
But the important thing is that
distance is not so special.

309
00:14:43,510 --> 00:14:45,430
And also, the details matter.

310
00:14:45,430 --> 00:14:47,890
So as you can see here, we can
get very different estimates

311
00:14:47,890 --> 00:14:50,150
based on where the
occupants are placed,

312
00:14:50,150 --> 00:14:52,400
how they're facing each
other, what kind of activities

313
00:14:52,400 --> 00:14:54,620
they're engaging in,
what kind of movements.

314
00:14:54,620 --> 00:14:57,220
So there's really no
universal guideline.

315
00:14:57,220 --> 00:14:59,560
It makes more sense to start
from a universal guideline

316
00:14:59,560 --> 00:15:03,010
for long-range transmission
and then enforce

317
00:15:03,010 --> 00:15:08,470
mask use in situations where we
are worried about transmission,

318
00:15:08,470 --> 00:15:10,930
rather than trying to guess
how people are going to behave

319
00:15:10,930 --> 00:15:12,550
and what kind of
distance they're going

320
00:15:12,550 --> 00:15:14,090
to keep not wearing masks.

321
00:15:14,090 --> 00:15:15,520
So the safest
thing is, if you're

322
00:15:15,520 --> 00:15:18,010
worried about
coronavirus transmission,

323
00:15:18,010 --> 00:15:21,510
just wear a mask,
indoors especially.

324
00:15:21,510 --> 00:15:25,230
So that brings us now to
thinking about summarizing

325
00:15:25,230 --> 00:15:27,900
this entire chapter, going
beyond the well-mixed room,

326
00:15:27,900 --> 00:15:30,450
where we've been discussing
the fluid mechanics

327
00:15:30,450 --> 00:15:35,280
of indoor spaces and of human
occupants and respiration

328
00:15:35,280 --> 00:15:37,360
within those spaces.

329
00:15:37,360 --> 00:15:42,240
So I think I'd like to leave
you with the picture of people

330
00:15:42,240 --> 00:15:44,200
who are smoking in the room.

331
00:15:44,200 --> 00:15:47,190
So we're all familiar
with the situation

332
00:15:47,190 --> 00:15:49,860
where you have a
room-- let's say,

333
00:15:49,860 --> 00:15:52,890
could be a restaurant
or some other space

334
00:15:52,890 --> 00:15:55,380
where there is,
let's say, a table

335
00:15:55,380 --> 00:15:56,880
or a few tables,
where there's maybe

336
00:15:56,880 --> 00:15:58,860
5 or 10 people in the room.

337
00:15:58,860 --> 00:16:01,830
And there's one person or
two people that are smoking.

338
00:16:01,830 --> 00:16:04,230
Now, we know that when
the person who's smoking

339
00:16:04,230 --> 00:16:06,360
breathes in on the
cigarette and exhales,

340
00:16:06,360 --> 00:16:09,300
there's a very dense plume
of smoke that comes out.

341
00:16:09,300 --> 00:16:12,630
It gets carried by thermal
currents and rises.

342
00:16:12,630 --> 00:16:15,720
And you know that if you
stand right in that space,

343
00:16:15,720 --> 00:16:17,890
it will be a very significant
amount of smoke you're

344
00:16:17,890 --> 00:16:18,930
going to have to breathe.

345
00:16:18,930 --> 00:16:20,940
In fact, it's courteous
for the person who's

346
00:16:20,940 --> 00:16:24,520
smoking to [EXHALES] breathe
away and not breathe directly

347
00:16:24,520 --> 00:16:25,520
in other people's faces.

348
00:16:25,520 --> 00:16:26,970
That would be sort of rude.

349
00:16:26,970 --> 00:16:30,240
And maybe, as we're thinking
about respiratory transmission

350
00:16:30,240 --> 00:16:32,730
of viral disease, we should
think in the same way.

351
00:16:32,730 --> 00:16:34,230
Each person should
be worried about,

352
00:16:34,230 --> 00:16:36,660
am I really breathing
directly on another person?

353
00:16:36,660 --> 00:16:39,690
If I'm not wearing a mask, why
don't I breathe somewhere else?

354
00:16:39,690 --> 00:16:42,240
But we also know
from our experience

355
00:16:42,240 --> 00:16:44,700
with smoke-filled rooms
that there may only

356
00:16:44,700 --> 00:16:46,020
be one or two people smoking.

357
00:16:46,020 --> 00:16:49,500
And you can occasionally see
these puffs or burst of smoke

358
00:16:49,500 --> 00:16:52,530
when they're exhaling after
drawing on a cigarette.

359
00:16:52,530 --> 00:16:54,870
But if you look around
the rest of the time,

360
00:16:54,870 --> 00:16:56,480
the smoke is kind
of swirling around.

361
00:16:56,480 --> 00:16:58,440
It's a little more
concentrated in some places.

362
00:16:58,440 --> 00:17:00,060
But you can see
very quickly, it's

363
00:17:00,060 --> 00:17:02,010
uniformly spread
throughout the room.

364
00:17:02,010 --> 00:17:04,200
And somebody who is on
the far side of the room

365
00:17:04,200 --> 00:17:07,380
is at essentially the same risk
as somebody who's very close--

366
00:17:07,380 --> 00:17:10,050
even 6 feet or 3
feet away, whatever

367
00:17:10,050 --> 00:17:12,060
that special distance may be--

368
00:17:12,060 --> 00:17:14,599
because the air is
typically well mixed.

369
00:17:14,599 --> 00:17:17,700
And those smoke particles
end up throughout the room.

370
00:17:17,700 --> 00:17:20,310
And you're just as
much risk at 60 feet

371
00:17:20,310 --> 00:17:23,500
as you are at 6 feet
under those circumstances.

372
00:17:23,500 --> 00:17:28,900
And so that's really the
main message of this course,

373
00:17:28,900 --> 00:17:31,920
while we also keep in mind that
there are these sort of details

374
00:17:31,920 --> 00:17:33,420
of short-range
transmission that I'd

375
00:17:33,420 --> 00:17:36,700
like you to be aware
of when applying

376
00:17:36,700 --> 00:17:40,820
the guideline for long-range
aerosol transmission.