[jlebar]

It's an amazing fact of mathematics that even a vaccine that has relatively low efficacy can completely neutralize transmission if enough people in a group take it.

This is especially true in the case of the flu because it has a relatively low R0 of approximately 1.3, meaning that without intervention/vaccines, each infected individual infects on average 1.3 other people. The vaccine just needs to be effective enough to drive the reproduction rate below 1 for the virus to die out.

We do not have good data on how effective flu vaccines are at neutralizing transmission. But for the sake of argument, let's take these relatively "bad" years for the flu where they prevented 40% of doctor's visits. Suppose that corresponds to merely preventing 40% of transmissions. The other 60% of transmissions still occur.

In that case is it even possible to drive R_eff (the effective reproduction rate of the virus) below 1? It turns out, yes! With an R0 of 1.3 and an effectiveness of only 40%, you stop the spread of the virus after vaccinating only 60% of people.

Details on the math: https://claude.ai/share/8e8ffef7-ba33-44aa-a2a6-ca3b9be6d516. You can also extend the conversation and ask more questions!