Mask-wearing and COVID-19 is complicated. And not just because it’s become politically
fraught, not just because there are many different kinds of masks of varying levels of effectiveness,
not just because there’s been a shortage of medical grade masks so authorities were
trying to convince the public not to buy them, not just because there’s tons of malicious
or simply misguided misinformation flying around, not just because our understanding
of how COVID spreads has been changing, and not just because countries in the West ignored
the lessons learned by Asian countries that faced SARS (though all of these things are
true). In addition to all this, masks are also complicated
because they fly in the face of our mathematical intuition. The good news is that when you do the math
(and we’re going to), you find that masks are much more effective than you might think. Say you have a mask that cuts in half the
chance a contagious person will infect a nearby susceptible person. In other words, this mask is 50% effective. Except, this mask is way more than 50% effective
because as we’ll see, when many people wear even just a 50% effective mask, you end up
with way more than 50% protection (both to the wearer and to society at large). It seems obvious that if no one wears a mask,
then no one gets any benefit - and that’s true. And you might assume that if everyone wears
a 50% effective mask, there’d be a 50% benefit - that is, a 50% drop in disease transmission. But that’s not how the math of masks works! When everyone wears a 50% effective mask,
disease transmission actually drops by 75% -- much better than 50%. Masks break our intuition because we’re
used to thinking about masks as single-directional, only protecting the wearer. But masks can protect in both directions,
when you breath in through them, and when you breath out. This means that when everyone is wearing masks,
there are in fact two masks between any two people. If we assume for simplicity that masks are
equally effective in either direction – and if this assumption bothers you, stick around
till the end of the video – if masks are equally effective in either direction, then
the first mask cuts disease transmission in half, and the second mask cuts it in half
again. So overall, you end up with a 75% drop in
disease transmission, not 50%. In this scenario, masks do double duty! But in reality, not everyone will wear a mask. So when a contagious person encounters a susceptible
person, there are in fact FOUR possible routes of infection. In the first route neither person is wearing
a mask, which means there’s no reduction in disease transmission. In the second route, only the contagious person
is wearing a mask, and so for a 50% effective mask, disease transmission drops by 50%. In the third route, only the susceptible person
is wearing a mask, and again disease transmission drops by 50%. And in the final route where both the contagious
person and the susceptible person are wearing masks, disease transmission gets cut in half
twice – aka it drops by 75%. What does this mean for society overall? Well, it depends on what fraction of people
wear masks. As we’ve seen, if no one wears masks then
no interactions involve any masks and the overall drop in disease transmission is 0%. And if 100% of people wear masks, then all
interactions involve two masks and the overall drop in disease transmission is 75%. But if 50% of people wear masks? Then on average – assuming that people interact
randomly – a quarter of all interactions will involve no masks, a quarter will have
the contagious person masked, a quarter will have the susceptible person masked, and a
quarter will have two masks. So even when just half of people wear masks,
three-quarters of interactions involve masks (and a significant portion of those involve
two masks). Do you see the magic math of masks yet? Your first guess might have been that if 50%
of people wore 50% effective masks, you’d get a 25% drop in disease transmission because
50% of 50% is 25%. In fact, this intuition would be true if masks
were only effective one-way (like on exhalation only) - then there’d just be two routes:
either the contagious person wears a mask, or they don’t, and these average to 25%. BUT when we take into account the two-way
nature of masks and average over all four possible mask combinations, the overall drop
in disease transmission becomes almost twice as good! Masks Work Better Than You’d Think. And this is true in general - no matter what
numbers you choose for mask effectiveness and usage, the overall drop in disease transmission
is always better than the intuitive guess from just multiplying those numbers together. So what does this mean for the 2020 pandemic? Well, for COVID-19, epidemiology suggests
that each contagious person infects on average 2.5 other people. If you could drop that number to below one,
a drop of just over 60%, then each contagious person would infect fewer than one other person
on average, which would be enough to swiftly halt the spread of COVID-19. So what would it take to drop disease transmission
by 60%? Well, there are many options, but a particularly
cost effective and arithmetically satisfying one is this -- if 60% of people wore 60% effective
masks, disease transmission would drop by 60%! And if we did that, we would beat COVID - the
mask math shows us how. Specifically, it shows us that masks are more
effective than you’d think for two reasons: first, they do double duty when both people
wear them, and second, the fraction of interactions involving masks is always much more than the
fraction of people who wear masks. This is the magic multiplicative power of
masks –– even partially effective masks, partially adopted, can extinguish an epidemic,
as long as enough people wear them. Ok, some caveats to all this:
We’ve been pretty vague about what it actually means for a mask to be X% effective --- for
the purposes of the math in this video, all that matters is that disease transmission
drops by X%, irrespective of how the mask actually achieves this drop. In reality, masks reduce disease transmission
through a combination of filtering and redirecting air, and they vary a lot in effectiveness
depending on their filtration, how tightly they fit, if they have an exhalation valve,
etc. So it’s hard to give exact numbers; a 50%
effective mask could be something like an N95 worn poorly (or incorrectly decontaminated)
or a cloth mask worn well. We’ve assumed that masks provide equivalent
protection upon inhalation and exhalation. Aatish put together an interactive essay where
you can see what happens when inhalation and exhalation effectivenesses differ, what happens
when more (or less) of the population uses masks, and more. For simplicity we’ve assumed that contagious
people are just as likely to wear masks as non-contagious people. We also assumed that people mix randomly,
which isn’t necessarily true. For various reasons, people who wear masks
may be more likely to interact with other mask wearers, and less likely to interact
with those who don't wear masks (and vice versa). Clustering non-mask users together diminishes
the overall protective power of masks and means you need more people to wear masks to
achieve the same drop in transmission. Again, if you’re interested in more details
and references, definitely check out the interactive companion essay at aatishb.com/howmaskswork. This video was made with the generous support
of the Heising-Simons Foundation, which normally works with MinutePhysics to help communicate
about fundamental physics research, but this year they’re providing additional funding
to focus on the response to COVID-19. That means they’ve supported research – including
some of the N95 mask decontamination work I mentioned in my video on the physics of
N95s – they’ve supported hospitals and remote learning, they’ve helped low-income
households maintain access to utilities, and they’re funding COVID science communication
like this video! A big thanks to Heising-Simons for their support
of science – both fundamental and applied – as well as science communication.
