Let’s do a little math – masks and delta COVID

A little basic math illustrates why masks still work even if the delta variant is surging

I keep running into COVID antimaskers online who are incorrectly claiming that a) masks don’t work (they do) and that b) the current surge of delta cases proves it. There are many sources available that disprove claim A, so I won’t bother trying to correct that false claim here. Instead, I’m going to focus on doing a little basic math (multiplying and diving by two) to illustrate why claim B is false.

Let’s start with a two facts and an assumption that we’ll use to make the math easier.

Fact #1: The alpha variant from last fall had a reproduction number, aka r0, of about 2.5. R0 is a rough measurement of how transmissible a virus is and it corresponds to the average number of people a sick person will infect without controls like vaccines, masks, social distancing, quarantines, etc. In the case of alpha, that means one sick person would infect an average of 2.5 other people.

Fact #2: The delta variant currently circulating has an r0 of about 5.0. Early data suggested it was more like 7-9, but a recent study (which may be low – the details are too new to say for sure) suggested it was more like 5. That’s 2x the r0 of the alpha variant.

Assumption: In order to make the math easy, let’s assume that masks are 50% effective. That means they drop the r0 by a factor of two. Again, this is just to make the math easy and doesn’t necessarily reflect the actual effectiveness of masks against COVID.

Now let’s look at what that would mean for the two different COVID surges and their respective variants.

Last fall, when the alpha variant was dominating, if everyone wore masks that were 50% effective, then the r0 for alpha would have dropped from 2.5 to 1.25. This would mean that one infected person would infect, on average, 1.25 other people. This is enough to have a pandemic, but it’s also not much worse than seasonal flu. Any value of r0 below 1.0 would mean that the pandemic was slowly dying out.

Now let’s look at the pandemic since roughly June, when the delta variant pretty much took over everywhere. With an r0 of 5.0, if we reduce that by 50% for everyone wearing masks, then we’d have an adjusted value of 2.5. Which, not coincidentally given this illustration, is the exact same as the alpha variant was without masks.

Just so we’re clear, if masks are 50% effective, they would have dramatically reduced the spread of the alpha variant last fall. But masks today would only slow the spread of the delta variant to the point that the alpha variant was without masks at all.

And this is what disproves claim B above. Instead of disproving the effectiveness of masks, the current surge in cases simply shows that the delta variant is way more transmissible than the alpha variant was. And that’s something we already knew.

This is a variant (pun intended) on the same argument I made about infection controls last October, when I pointed out that masking and other controls could completely shut down the flu while still fail to control COVID. The only difference here is that we’re talking about two different COVID variants, not two entirely different viruses.

My math is illustrative only – I don’t know if masks actually are 50% effective or not, I just assumed they were for the purposes of illustrating the fundamental flaw in claim B above. But I’d guess that public health departments in counties and states across the country are doing the same kinds of calculations with more accurate numbers than my guess and reaching very similar conclusions. Given how fast the virus has been spreading, it’s hard to imagine otherwise.