# 33

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.

# 33

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When correcting non-experts for using the wrong metrics, I think it is more important to supply them with the metric that accurately captures their point, rather than just explaining why the original metric they chose was wrong.

This is a good post, and I not only learned from it but was motivated to review the CDC’s more in depth description of R0 as well.

I suspect what your COVID-cautious dance coordinator was trying to express was that in a community dance setting, the amount of social contact is higher than what is built into models of Rt and R0. Neither number will fully characterize the risk of going to a dance, and it’s not just that we’ll be “somewhere in between” - we are just working with a whole different model at that point than was used to generate these figures.

If it was up to me, I might try and communicate about the risk by talking about physical world modeling - “we’ll be in close contact for hours, breathing each others’ air, and there are a lot of older folks who come to community dancing. We keep this dance masked to help blunt the increased risk this poses.” This lets you explain your rationale in a way anybody can understand, without the risk of miscommunicating the science.

I guess the person assumed that R0 is an immutable property of the virus, which reminds me of Eliezer's old post on fictional aliens invariably having the same beauty standards as modern Western heterosexual males.

Huh? R0 is immutable.

R0 is not remotely immutable. It is a function of people's behaviour and physical infrastructure as well as physical properties of the virus (which are themselves likely changing, especially early in a pandemic, as the virus evolves).

It is not affected by levels of exposure, because R0 is defined as the infection rate in the absence of any exposure.

'Immutable' is a tricky word. Let's be more specific about what R0 does and doesn't include:

• Viral evolution: yes (ex: R0 for Omicron is higher than R0 for Delta)
• Immunity from vaccination against this pathogen: no
• Immunity from prior infection by this pathogen: no
• Immunity from vaccination for or prior infection by other pathogens: varies depending on how close the other pathogens are and whether we consider this to be one long outbreak or several (this generally doesn't seem very principled)
• General behavior of the population: yes (ex: R0 is lower in populations that socialize mostly outdoors)
• Behavior changes in response to this pathogen: usually no (ex: people moving socializing outdoors or starting masking in response to this virus does not decrease its R0, except that some papers define it differently so that it does)

I think maybe a lot of the disagreement here is whether you consider these to be R0 changing vs different R0s for different scenarios?

Overall, this means that if you're going to use the R0 from a paper it's worth putting a good bit of effort into seeing how this particular paper is using it.

It'll tend to change with things population, social conventions, etc.  For the herd animal populations it was originally applied to you can pretty much ignore all of that but not for humans.  Especially for things like coronaviruses with a high k where R0 is driven by the fat tail of the distribution.  In a small village where most bat/human coronavirus crossovers tend to happen the village size limits how large a superspreader event can be.  Not so in a city.  And then you have things like Ebola spread being partially driven by funereal customs.

I guess a better way of putting that is that R0 is fixed for a particular population but humans are composed of many different populations, just like there are other populations of different species a virus can also infect which might have their own R0s as well.

Only "in a population that has not previously encountered the disease", which no longer applies to this planet.

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This, and a different case where another one of the most covid cautious organizers had the trajectory of death rates backwards, has me wondering how much of the caution is driven by misunderstandings of the risk.

On the other hand, I don't think there's any reason to expect that misunderstandings are more likely on the cautious side, so probably organizers that are especially unconcerned about covid are also misunderstanding risks?