How masks work: It’s simple arithmetic

Published: 7/30/2020 7:32:00 AM

Covid-19 is spread as infected people exhale, cough, sing, shout, or sneeze in the vicinity of others, who may then become infected. For the sake of argument, let’s make two assumptions: (A) Without taking precautionary or preventive measures, an infected person will infect, on average, two more people. (B) It takes a week for the infection to take hold, at which point a newly infected person can infect others. The disease would then progress as follows:

Week 0: 1 person becomes infected and passes the disease to

Week 1: 2 more people, who infect

Week 2: 4 people, who infect

Week 3: 8 people, who infect

Week 4: 16 people, who infect

Week 5: 32 people, who infect

Week 6: 64 people, who infect

Week 7: 128 people, who infect

Week 8: 256 people.

Thus, at the end of two months there will have been a total of 511 cases. The current ratio of deaths to total cases in the U.S. is approximately 0.4%. At this rate, it is likely that two people will have died.

Now let’s assume that wearing masks cuts the infection rate in half. You might at first assume that in two months, then, there would be half as many, or 256, cases. But, no! Starting with that same first person infected, here is what happens if everyone wears a mask:

Week 0: 1 person becomes infected and passes the disease to

Week 1: 1 more person, who infects

Week 2: 1 more person, who infects

Week 3: 1 more person, who infects

Week 4: 1 more person, who infects

Week 5: 1 more person, who infects

Week 6: 1 more person, who infects

Week 7: 1 more person, who infects

Week 8: 1 more person.

Thus, at the end of two months, there will have been a total of nine cases. At the mortality rate of 0.4%, it is likely that no one has yet died. Therefore, if you are that very first person, by wearing a mask you have prevented 502 people from getting ill, and you have saved the lives of at least two people.

So, whether or not your nation, state, county, city, town, or book group says you have to wear a mask, you really should wear a mask. You will feel better for it, and so will 502 others.

John K. Bollard is an editor, translator, lexicographer, and occasional professor of English and Medieval Welsh who lives in Florence.


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