Fig. 2.

Comparison between herd immunity estimates from age and contact structured model (Model 1) and a simple SIR model. The age and contact structured model is very similar to a simple SIR model in terms of the fraction of the population that must either be infected naturally (in the $E$, $I$ or $R$ classes) or vaccinated successfully in order for the number of infections to begin to decline. This is the so-called “herd immunity” fraction. The theoretical result (blue) is simply $1-1/R_0$. The model result is obtained by running a simulation at the given $R_0$, as always defined in the absence of vaccination, detecting when infections begin to decline, and obtaining the portion of the population either infected or successfully vaccinated at that time. (Recall that Model 1 does not account for immune evasion).