With R_0 of 2, you need to have 50% immune to have herd immunity, but in practice, you’ll have more people than that that will end up infected before the epidem

With R_0 of 2, you need to have 50% immune to have herd immunity, but in practice, you’ll have more people than that that will end up infected before the epidemics dies out. Think about it: when over 50% of people get and survive the disease, rendering them immune, the epidemics doesn’t just immediately stop. What happens instead is that since average sick person transmits it to 2 people, but one of them is immune, less than one person gets the disease, and the epidemics starts the exponential die-out. However, as it dies, people still get infected, albeit slower and slower until it stops altogether. The epidemics final size equation is F = 1 - exp(R_0 F). For R_0 = 2, F is around 80%, despite the herd immunity kicking in already at 50%.