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Comment by jonplackett | Hacker News Reader

I really don’t get why this is still considered a conundrum

Lots of places have R hovering around 1. If it goes to 1.1 everything goes to shit, if it drops to 0.9. Everything will be fine.

So even if masks reduce spread by a tiny amount, even 10% better. That could easily swing you below 1 and save the day.

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The trouble is that this doesn't actually work. By using R this way you're assuming a model where every person is equally likely to spread the infection to every other person in the population, which is easy to calculate but what actually happens. In reality people can only spread the virus to those they're in contact with, and (say) a supermarket employee can spread the virus to more people than someone working from home and not socializing due to social distancing rules. Not only that, there are clusters of people who are all likely to spread the virus to more people or to less people when infected, such as workers in food manufacturing, people in dense urban areas vs less dense areas, etc...

So what actually happens in reality is that if R is hovering around 1, there are going to be some places where it's actually above 1 and cases are growing exponentially, and some where it's below 1 and they're shrinking exponentially. The end result of this is that places where R is actually below 1 make up an exponentially shrinking proportion of all cases, and as this happens it causes the overall measurement of R to go back above 1.

Ok, makes sense. But why does this make any difference to the crux of my argument? - if that supermarket employee is wearing a mask, they’re going to spread it to less people.

R=1.1=everything goes to shit is not a valid inference. R is just the derivative of the case graph. It can and does change on a daily basis, says nothing about absolute levels, and says nothing about how it will evolve over time or what the actual peak levels of infections will be. You can find "exponential growth" in nearly any graph if you want, look at a sine wave for example, and viruses in particular are a curious choice to describe this way because epidemics show S-curve logistic growth, not exponential. It's very confusing to people that it's so often described as exponential because that implies unbounded and very rapid doubling until a day/serial interval before saturation half the population is infected at once, whereas we know that epidemics don't do that in reality.

Ok so what I mean is r being 1.1... over time.

I think you’re looking to find holes in a perfectly reasonable argument by adding complexity.

Over how much time and how does that variable relate to the actual length of time an epidemic of an (apparently) seasonal respiratory virus is expected to last?

I don't think it's just a nitpicky minor thing. Governments have pretty regularly been making decisions and citing the value of "R" (they mean Rt), or "exponential growth", as a justification for new restrictions, apparently without realizing that by itself these things means little and justify nothing. Exponential growth can only be said to be a problem when taking into account the serial interval, the actual exponent, the starting population sizes, total population sizes, fixed capacity limits (e.g. hospital bed counts) and so on. Yet the scientists advising governments routinely ignore all those things.

10% would not be tiny, that would be a statistically huge percentage based on population counts.

The CDC study concluded 2% reduction. That’s in the range where harms need to be weighed too (e.g. masks that aren’t replaced often enough harbor bacteria themselves; there’s environmental costs, etc)

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