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  • 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 directionand

  • if this assumption bothers you, stick around till the end of the videoif 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 twiceaka 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 averageassuming 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 researchincluding 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 scienceboth fundamental and applied

  • as well as science communication.

Mask-wearing and COVID-19 is complicated.

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B1 mask transmission disease effective contagious drop

Why Masks Work BETTER Than You'd Think

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    Summer posted on 2020/09/08
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