Why Face Masks Work

While I started advocating the use of face masks and other measures to contain COVID-19 a while ago, I must admit that I was surprised with more recent evidence that face masks work very well to stop new COVID-19 infections.

So I have been thinking about why face masks that may only capture 50% to 80% of virus particles could have such a large effect. One often-heard argument is that fabric and self-made "face masks don't work", because they do not capture very small droplets, and because they often do not fit well, so that a lot of air breathed in or out goes around the mask, rather than through the mask.

But a reflection about what scientists have learned over the last few months provides a good explanation on why face mask can have a huge impact on the COVID-19 pandemic, even if they "capture" only 50% of the virus particles in exhaled droplets.

In recent weeks, it has become increasingly obvious that transmission through airborne virus particles that are emitted when talking, singing, and breathing play a very important role in COVID-19 transmission. Many "superspreader" events where one person infected dozens of others in a short time frame can only be explained through aerosol transmission; choir practice events, where often more than half of the attending singers got infected, are one example.

A game of chance: the "Independent Action Hypothesis"

To understand what is going on, we need to look at the biology underlying COVID-19. When someone breathes in air that contains small, virus-containing droplets suspended in the air, the virus gets deposited on mucous membranes in the nose, throat, and lungs. From then on, it's a race: the virus needs to find a cell that it can infect; infect the cell and multiply; and then be excreted from the cell in large numbers, to find new cells and infect them. Repeating this cycle, the virus eventually is present in the infected body in billions of copies.

But there's many things that can go wrong. At body temperature, the virus is not very stable, and looses its ability to infect after some time. We do not know exactly what this time is, but the data we have is that it's somewhere in the range between a few minutes and perhaps a couple of hours. Furthermore, the human body is not defenseless: it has many different molecules and cells participating in the "innate immune response" that can "kill" the virus (the "kill" is in quotes because a virus does not meet the formal definition of being alive - but it's easy to understand).

So when a single viable virus particle enters the body, there is a chance that this will lead to a full-blown COVID-19 infection - but that chance is probably very small, perhaps 1 in a 1000 (we do not actually know this number, but 1 in 1,000 is a common guess). But as more virus particles enter the body, the chances of establishing a successful infection increase. If it's 10 particles, chances of "success" go up to (about) 10 in 1,000, or 1 in 100; if it's 100 particles, they rise to about 100 in 1,000, or 10%. If 1,000 virus particles enter the body, the chance of success get close to 100% (not exactly 100%, if you'd look at the probability statistics, but close enough for this discussion).

What I described above is called the "Independent Action Hypothesis". We actually do not know for a fact that it applies to COVID-19, but many scientists believe that it applies because it is the most plausible hypothesis.

"Attack rates" within the same household and at "superspreader events"

Next, we need to look at two important questions:

1. What percentage of people in a household get infected in one person has COVID-19?
2. Can everybody get infected?

A number of different studies have looked at how likely it is that someone in the same household gets infected if one family member had COVID-19. The actual results vary, but usually falls somewhere in the range between 20% and 60%. In most, if not all, studies, not everybody in the household got infected. Which brings us to the second question: can everybody get infected? Household studies do not give a good answer to this question, because once a person begins to show COVID-19 symptoms, others in the household are likely to be more careful about keeping their distance, washing hands, and so on, to avoid getting infected.

Instead, we can look at "superspreader" events, where a well-defined group was exposed to one or more COVID-19 patients. Cruise ships are one example that caught a lot of attention early in the epidemic, but may lead to false conclusions: as soon as the first likely cases on cruise ships were diagnosed, the passengers typically were isolated in their cabins, which significantly reduced further transmissions.

But there are several other events in the database of COVID-19 clusters, which includes many superspreader events, that provide a better answer. On a French navy ship 61.9% of soldiers ended up with COVID-19 - a total of 1,081 cases. A choir practice in Washington lead to attack rates of 75-80%, and other choir practice events led to similar infection rates. From such events, we have evidence that at least 60% to 80% of people can get infected with COVID-19.

If we put these two bits of information together, we can conclude that exposures to the corona virus often happen at levels where an infection can happen, but only sometimes happen at levels that are so high that just about everyone who can get infected does get infected. For example, if a typical household exposure would consist of 200 virus particles, then we'd expect an infection rate of about 20% - roughly what was reported in some studies.

How even "bad" masks reduce COVID-19 transmissions by 50% to 75%

Let's do a little Gedankenexperiment, where we have three groups of 100 people each that get exposed to COVID-19. In all groups, each person is exposed to an infected person for exactly the time if would take to transmit 200 virus particles.

In group 1, neither the infector nor the infectee wear a face mask, so the infectee receives 200 virus particles. This results in 20 new infections.

In group 2, only the infector wears a mask. The mask is pretty bad and lets 50% of the virus particles through. Therefore, each infectee receives 100 virus particles. This results in 10 new infections - a 50% reduction.

In group 3, both the infector and the infectee wear a "50% reduction" mask. Each infectee receives 50 virus particles, resulting in a total of 5 new infections. The overall reduction of new COVID-19 cases is 75%.

The numbers above are just intended as examples. The scenario is also simplified; reality would typically include different exposure levels for different people, and other variables. But even with further refinements, it is plausible that a large number of COVID-19 infections happen at levels where the likelihood of infection is directly proportional to the number of virus particles a person is exposed to, and that reducing the number of virus particles by using "bad" face masks can still have a large effect.

In the context of an epidemic, what is basically a linear effect on an individual level can be a much larger effect on the growth rate of the epidemic. For example, if the effective growth rate R is 2.0 without mask, but mask use reduces transmissions by 50%, that would convert the growth from exponential to stationary with R = 1.0. A reduction by 75%, as in the "group3" example above, would lead to R=0.5, and a rapidly shrinking number of new transmissions.

But ...

isn't that too simple? Indeed, I made a number of simplifications above. Also, the analysis often relies on assumptions where we do not have actual data. But the assumptions I made are more reasonable than most, if not all, alternative assumptions (for example a "threshold level" hypothesis instead of the "Independent Action" hypothesis). However, the general conclusion that many transmission happen in the "linear dose-response range" matches many observations made in recent months about COVID-19 transmissions, and what we have learned about the underlying mechanics. If you'd like a more formal analysis, check out the publication titled "To mask or not to mask: Modeling the potential for face mask use by the general public to curtail the COVID-19 pandemic" that came to very similar conclusions.

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Note added 6/29/2020:

In the week since I wrote this post, several new studies describe empirical evidence that face masks are effective to reduce COVID-19 transmissions.

One study, titled "Data-driven estimation of change points reveal correlation between face mask use and accelerated curtailing of the COVID-19 epidemic in Italy", showed that the number of new COVID-19 infections declined faster after masks became mandatory, and concluded that "widespread use of face masks and other protective means has contributed substantially to keeping the number of new Italian COVID-19 cases under control in spite of society turning towards a new normality".

A second study titled "Face Masks Considerably Reduce Covid-19 Cases in Germany" looked at different regions in Germany, where face mask use became mandatory at different dates. It concluded "face masks reduce the daily growth rate of reported infections by around 40%".

Faced with a mounting body of scientific evidence that face masks work, and very rapid growth of new COVID-19 infections in many southern states, even "leading Republicans are publicly embracing expert-recommended face masks as a means to slowing the spread of the deadly coronavirus", according to an NPR article, leaving President Trump and Vice President Pence increasingly isolated in their opposition against wearing face masks.