PROFESSOR: So now let's summarize
where we've come to in our analysis of short-range effects
from respiratory jets relative to long range
airborne transmission which we previously calculated.
And let's also think about what are
the implications for policy.
And for personal decisions about safety during the pandemic.
So first of all, when masks are worn,
we've already discussed the filtering effect of masks.
We've talked about how that brings
a squared factor of the mask penetration factor
which leads to a very substantial increase
in the reduction in the transmission rate.
But there's another important factor
when you have a mask, even a fairly poor mask, a cloth mask,
it may not be so great a blocking aerosol particles
but it's very good at blocking momentum
so the fluid momentum that comes from just normal breathing
is almost completely stopped by a mask.
Even a vigorous cough only lets some momentum through
and a few droplets from more violent activities
such as that.
So what's more typical in a case where people are wearing masks
is that there is sort of some exhaled air slowly
building up around you without very much additional momentum.
And as we've discussed that air is warmer and tends to rise.
And so typically the thermal plume
of kind of the exhaled air rising above you a bit
like a chimney and that's where the droplets initially reside.
We're not likely to directly infect anybody by that method,
either because people aren't close enough
or they aren't above the other person.
And then, of course, there are other flows
in the room that we've discussed,
which are often turbulent.
And those will transport the droplets everywhere
and will lead to the well-mixed room
as being the most natural and most accurate
first approximation for the infection risk
by another person who is also wearing a mask.
So I would argue that no strict social distancing is
required in a mask situation.
So whether we're six feet or three feet,
it's not going to give us substantially more safety
if people are wearing masks.
And instead we should pay much more attention to the formula
that I boxed here, which gives you
an estimate of the long range transmission risks airborne
which is equally there for everyone in the room.
And that must be considered for safety
and also for contact tracing.
Now situation is very different without masks.
As we've seen without masks, we are imparting a lot of momentum
to the fluid, the air.
Simply by breathing and certainly
by talking or singing or exercising,
we're really pushing the air around and launching
those particles into the air.
And even at three feet or six feet
there can be still a substantial risk.
Although as we said, the difference
between three and six is not so great.
So one might consider switching to three.
On the other, hand, even six may not
be enough protection you might need to be thinking
about longer distancing.
And of course, there is always the airborne risk.
So at some point, you hit that point x_c
where the airborne risk is comparable to the short-range
risk.
And also there are people such as the guy I sketched back here
which are not in the respiratory jet
and probably have a lower risk than the average.
So it's definitely important to still consider
the average risk coming from the long range guideline.
But one could add a correction to be very conservative
for cases such as sketched here when this poor person is
finding himself or herself in the respiratory jet
for long periods of time.
So let's imagine there's a typical spacing, x bar, which
would be sort of the worst case but still
typical spacing one might expect of the people in the rooms.
If you think there's a certain situation where
maybe two of the people might be five feet apart or four,
three feet apart and facing each other
for sniffing amounts of time, and then p jet
is the probability that they are encountering
each other's respiratory jets.
Or maybe put another way, the fraction
of the time one person spends in another person's
respiratory jet.
When that happens the transmission
is just between two people.
It's not to the entire room.
So that's another very important factor to keep in mind,
this factor of n, the occupancy, doesn't really
come up in the social distancing model
here when we're talking about the indoor reproductive number.
So to make a modified guideline, we
can take the long range indoor reproductive number
and add a short range correction.
We've already calculated what this looks like.
So if I write the guideline as n minus 1 tau
is less than epsilon over the average beta,
I can also restore what that means here.
Average beta times tau is the integral, time interval data,
basically, of the transmission rate.
And so this fact that we've already
calculated the ratio of the shortrange term
to the longer term is x_c over x--
or x bar times p jet.
It's a very simple correction.
If we plug back in our estimates for this average beta then
we arrive at this formula here.
The first term is the same guideline we already have.
And there's a new term now which, notice,
does not involve n and doesn't have the mass factor,
of course, as well.
But it involves the length, so social distancing.
And it involves the mouth area and the breathing rate.
The breathing rate now is also not
coming in square because we're assuming
that the breath is already providing this concentration.
And we're just looking at another distance downstream.
And the Qb is for the receiving person's inhaling breath rate
whereas the QB squared comes from inhaling and exhaling
and finding the steady state in the room.
And so we've already estimated how big
this term is [? xc ?] over x might be anywhere
from one to 100 or maybe even 1,000 if you let p jet be 1.
So if you stand facing another person continuously,
this can be a large term and can actually dominate the other.
I'll notice there's an n there.
So still, there could be a balance.
But when you take into account that people are not always
directly facing each other so much,
then this number might be a lot smaller.
And I would argue that in many cases
the dominant term is the long range one.
And the short range one is the correction.
But one should be aware of situations
where the short-range effect could be dominant.
And so that must also be considered.
And this modified guideline here would be one way
to take that into account.