### R0 Is Not Counterfactual

April 13th, 2023
covid-19
Someone who helps organize an N95-required dance recently wrote to a group of organizers:

R0 is the number of people that an infected individual is likely to infect. R0 was 5.4 in Dec 2022. ... People who assume increased risk for themselves are also assuming increased risk for 5.4 other people.

This is wrong in two main ways, and I responded on the list, but I wanted to share my response here as well because the claim illustrates two common misconceptions.

The first issue is that R0 is for an entirely "susceptible" population, one in which no one has any gained any immunity from exposure or vaccination. What an R0 of 5.4 would mean is that if it had suddenly appeared in 2019, each infected person would on average infect 5.4 others. This is very different from the current situation where most people have had several shots, plus most people have had covid at least once. The term for the expected number of people an infected person will directly infect given current conditions is Rt, currently about 1. Which is really just another way of saying that covid levels have been changing relatively slowly: if Rt were 5.4 we'd have rapid growth tearing through the population.

The other issue is that even Rt doesn't tell you how many infections you getting sick would cause. You may know various things about your behavior that make the expected number of people you'd directly infect higher or lower, but that's not the main issue. Instead it's that (a) people you infect can go on to infect other people and (b) people you infect might otherwise have been infected by other people. These two factors push in opposite directions, but both can be quite large. Here are a pair of toy situations showing how, holding Rt fixed, one infection can lead to either very many or almost no counterfactual infections:

• A new epidemic is starting, and Rt (which is R0 in this case) is 5.4. There are very clear symptoms, and people are just starting to catch on. Very soon there will be massive behavior changes to suppress Rt, and at this stage those might or might not be enough. One more person getting infected could have a 5% impact on the chance that this becomes a pandemic infecting ~half the world. In which case the expected number of additional infections is ~200M people. Here (a) is the main factor.

• An new pandemic is well under way, and it has easily missed symptoms. Even with lots of precautions in place, Rt is still a very high 5.4. There are so many paths by which a person can get infected that one additional infection has almost no effect on how many people eventually get infected. Here (b) is the main factor.

Now, "how many counterfactual infections would I cause if I got sick", and "how would my getting sick shift the distribution of when other people get sick" are really valuable questions to know the answers to if you're trying to understand the social impacts of more risky behavior, and it would be great if we did know these. But the progress epidemiologists have put into estimating R0 is not most of what you'd draw on in trying to get better answers.

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