system
Given the following post, respond as if you're commenting on Reddit:
human
When a virus has an R0 of >1, why does it not just grow exponentially until it has infected all of humanity?

People are saying the Wuhan virus has an R0 of around 3.  I’ve heard R0 explained as the average number of people and infected person infects. Thus, it would seem that as long as this number is >1,  the disease would just spread exponentially ad infinitum until the entire population had been infected or enough had grown immune/been quarantined that the R0 fell below 1. In the case of Wuhan, the entire world population should be infected at around 21 iterations if the number of cases tripled each iteration (3^21 ≈ 10bil).

However, given that basically every virus had R0 of >1 and not all of humanity has had every virus, this doesn’t appear to be how it actually works. What am I missing here?
gpt
There's another variable used called R(effective) which takes into account the number of people who can't catch the virus. For example, some people might have caught it before and are immune to it or may have been vaccinated. R(eff) = R0 • (the fraction of people susceptible). When nobody has immunity, for example when the virus is new, R(eff) ~= R0 but as immunity grows R(eff) gets lower and lower.

Some others mentioned it but basically R0 is the number of people that the infected person will *possibly infect.* Say R0 is 2. So if one person out of ten has the virus, they'll infect two. At the same time, that one person will have gotten over the sickness and won't be infectable. So, since 2/10 people are already infected and 1/10 is immune, that leaves seven people. Usually, those two people would each infect two of the remaining seven, but what if instead they "infect" each other or the immune person? Suddenly R0 doesn't work as well as a model.

Edit to add: now R(eff) works better:

R(eff) = R0 • the fraction of people susceptible

R(eff) = 2 • (7/10) = 1.4 so the virus isn't spreading quite as fast any more

When you scale that up to humanity, there's a high chance that not everyone will catch the virus. Add onto that countermeasures like manditory bed rest, quarantine, vaccines, etc. and the virus can't find enough hosts to continue to propagate :)