Fig. 3.

Illustration ofTheorem 2.1. The cumulative density function (cdf) for the total proportion ever infected (effectively the integral of Fig. 2). For small ${\mathrm{ℛ}}_0$, all outbreaks die out without affecting a sizable portion of the population. For larger ${\mathrm{ℛ}}_0$, there are many small outbreaks and many large outbreaks, but very few outbreaks in between, so the cdf is flat in this range. The height of this plateau is the probability the outbreak dies out while small. This is approximately the predicted extinction probability for an infinite population (dashed). The probability of a small outbreak is different for the different offspring distributions, but the proportion infected corresponding to epidemics is the same (for given ${\mathrm{ℛ}}_0$).