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PROFESSOR: So now that we have
a fully parameterized safety

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guideline for indoor
spaces to limit

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the transmission
of COVID-19, we can

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go through some case studies.

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And I encourage you
to use the guideline,

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in the form of the spreadsheet
or the online app which

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are provided, to check out your
own space to see how you might

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mitigate transmission there.

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So here are two
representative examples

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of great interest today.

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So the first is a classroom
in the United States, which

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is very relevant for discussions
about closing or reopening

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or partially reopening our
schools during the pandemic.

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And the second example will
be that of a nursing home,

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which is a tragic situation
of great interest,

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because a large fraction--
in fact, almost half--

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of all deaths have occurred
in nursing homes and eldercare

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facilities here in
the United States,

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and a very significant
number around the world.

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So first, let's look
at the classroom case.

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So if we apply the
guideline, first of all,

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we see the typical shape
of what is predicted

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in a plot of occupancy
versus time, which

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is a curve with roughly
a 1 over x type behavior,

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because it is the product of
occupancy and time essentially

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that are limited
by the guideline.

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So you trade one for the other.

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So we have here
curves representing

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natural ventilation,
which we estimate

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to be an air change time of
around 3 per hour-- or 0.3.

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Excuse me-- so a
3-hour air change time,

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and also mechanical ventilation,
in this case with 8 air changes

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per hour, so reasonably
good mechanical ventilation,

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which is the red curve--

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the blue curve
being the natural.

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And this is in a
typical classroom

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space of 900 square feet
and 12-foot-high ceilings,

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so for the United States.

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And in such spaces,
the typical occupancy

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might be around
20 or 25 students.

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And so 20 students is
actually indicated here

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as the normal occupancy
for this space.

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And so what we see is
that the normal occupancy

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is safe for a certain
amount of time.

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But then eventually,
it becomes unsafe.

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And so in the case of lower
ventilation, of course,

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that transition
happens more-- sooner.

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And if you have
better ventilation,

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you can extend that time.

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Also in the dotted line here
is shown the transient solution

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in the guideline, which
accounts for the buildup

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of infectious aerosols when
an infected person first

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enters the space.

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And you can see
in this case, that

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buys you just a little
bit of extra time only

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in the case of the
natural ventilation,

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but really not much in the
case of mechanical ventilation,

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where the transient and
steady state curve essentially

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overlap.

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We can also compare this
with some typical official

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guidelines here in the United
States and also elsewhere.

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So first, we have
the 6-foot rule.

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And what we see is that
after a fairly short time,

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the 6-foot rule becomes
inadequate in the case

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of natural ventilation.

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In the case of
mechanical ventilation,

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still at some point, the
6-foot rule is unsafe.

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However, before that
transition happens,

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it's actually overkill.

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So for enforcing
the 6-foot rule,

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we are keeping people at
a fairly low density when

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perhaps that's not necessary
for airborne transmission,

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especially if masks
are being worn,

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because that cuts down the
short-range transmission

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and droplet transmission
that we've discussed.

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And airborne transmission,
analyzed by the guideline,

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is expected to be the
dominant mode of transmission.

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So the way this
plot is made is also

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allowing for rescaling
by the use of masks.

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So and also, by--

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so that's the horizontal axis.

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So what is plotted here
is the mask-adjusted time,

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which is pm squared times tau.

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So pm is the masked
transmission factor.

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So a very good mask
has pm near 0--

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for example, maybe 0.05 or even
0.01 for a good surgical mask,

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maybe 50% or 30% for a
decent cloth face covering.

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And so that comes in squared.

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And that factor
rescales the time.

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So for example, we see
here with ventilation,

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we might expect to get
40 hours in this case

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with the 6-foot rule, or if
we're at normal occupancy,

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maybe 20 hours.

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But if we have good masks
that have pm squared maybe

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on the order of 100, let's say,
or even 1,000-- so depending

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on what that value is-- you
see you can turn that 20

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hours into thousands of hours.

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And so it actually becomes quite
safe to stay in that space.

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Now, on the vertical axis, we
have the occupancy limit scaled

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by epsilon, the risk tolerance.

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So what's shown here, then,
is effectively risk tolerance

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of 1, which we would not want.

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We don't want any transmissions.

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But if you reduce that to
epsilon of 0.1 or even 0.01,

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then you again pick up
a factor of, let's say,

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10 to 100 reduction in
the time or the occupancy.

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But again, with masks, that's
offset by a factor which

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is typically larger than that.

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So what we're seeing
here is that even

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in a very conservative
viewpoint,

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if we analyze a
classroom space--

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where there by the way is no
filtration or other mitigation

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measures occurring
except for ventilation

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at either of these rates--

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we see that if masks
are worn consistently

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that we should be able
to get tens or even

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hundreds of hours of
shared use of that space,

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even at normal occupancy.

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Now, how should we
interpret that time?

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So the time could be a
continuous occupancy time.

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But especially if we're
looking at the steady state

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value, which is
more conservative

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than the transient,
then we can simply

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add up the cumulative time
that people spend together

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in the presence of
an infected person.

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And so if we get
to a number like,

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for example, 40 hours,
which we can easily

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achieve wearing masks
with normal occupancy

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and decent
ventilation, then that

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might correspond to one
week in the classroom

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with an infected person.

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That's a very good number,
because the time to symptoms

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is around five or six
days with COVID-19.

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Now, of course, some
transitions may be symptomless.

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But the recovery time is also
on the order of maybe two weeks.

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And so if you can stay
during that period of time

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in the presence of
an infected person,

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that infected person
essentially will

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be removed, either by
recovery or by showing

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symptoms and hopefully removing
themselves and going home.

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Also, this kind of analysis
can inform testing.

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If the guideline
says that you're

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safe for a week or even two
weeks of occupancy, given

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the number of hours per day
and the other conditions,

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and the testing frequency is,
let's say, once per week--

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and also we know that the
most infectious time only

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happens after, say, five
or six days after becoming

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infected-- then with weekly
testing and mask use,

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this becomes an
extremely safe situation

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from the perspective of
airborne transmission

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if people are wearing masks
carefully during that time.

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So that's one way to think
about these guidelines.

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Also, the guideline can tell you
the relative risk improvement

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if you, say,
introduce filtration,

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or you change the
humidity of the room

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or change the ventilation rate
other than values shown here.

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And you can play with the
spreadsheet or the online app

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to see how those
changes can take place.

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Our next example
is a nursing home.

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Now, here, I've-- instead
of scaling to epsilon,

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the risk tolerance, I've
just chosen a risk tolerance

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of 0.01, which is a 1% risk
of transmission if an infected

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person were to enter this space.

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You may want to take even a
smaller value, to be even more

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conservative, given
the grave danger

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that persons who
are in nursing homes

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are facing, partly
due to their age

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and also due to the
common situation

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of pre-existing conditions,
given that in many cases,

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there may only be months
or years left of life

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expectancy for those people.

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And so they are, in fact, at
the highest risk for COVID-19.

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So you want to pick
a very small epsilon.

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And so now, if you
look at these curves,

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then you see the horizontal
axis has now changed to minutes.

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So that's if no one is
wearing a mask, then

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on the order of minutes--

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so something like
the 15-minute rule--

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you can see there becomes
a risk of infection,

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although ventilation can
help and can turn the 15

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minutes, say, into 30 minutes.

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If we look at, say,
the 6-foot rule,

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which is shown here,
which would only

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place two people in a
typical nursing home room

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that we have just shown here--
so that would be two beds,

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although in some cases, as
in the example shown here,

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which is based on New
York City nursing homes,

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the size of the space
that we've assumed here

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would actually have a normal
maximum occupancy of three.

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So there could even be
three beds in this space.

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And the point is that even if
these beds are 6 feet apart,

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if the people are
not wearing masks--

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or if a person enters the
room, who is infected,

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who is not wearing a mask--

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the risk of transmission
is actually very high.

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And if people spend
long periods of time

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without masks, as many
nursing home patients must

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do because they have
trouble breathing already--

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so unless they're
on a respirator,

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if they're just kind of
in relatively good shape,

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they will be
breathing oftentimes

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for long periods without masks.

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And that can be
a serious problem

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and lead to very high risk.

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So the guideline
essentially helps

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to sound the alarm for
those sorts of situations

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and helps those facilities and
the caregivers design the space

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and the time spent in the
space with different people

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in a way that can help
to protect the residents,

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and also when combined with
testing and other mitigation

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measures, can hopefully reduce
the spread of the disease

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where it matters the most and
has led to the most deaths.