Fig. 2.

Simulated outcomes of SIR outbreaks in populations as described in Example 2.2. Outbreaks tend to be either small or large. The typical number infected in small outbreaks (insets) is affected by the details of the offspring distribution, but not the population size. The typical proportion infected in large outbreaks (epidemics) appears to depend on the average number of transmissions an individual causes, but not the population size or the offspring distribution. These observations will be explained later. These simulations are reused throughout this section to show how PGFs capture different properties of the distributions.