Size of outbreaks near the epidemic threshold

The spread of infectious diseases near the epidemic threshold is investigated. Scaling laws for the size and the duration of outbreaks originating from a single infected individual in a large susceptible population are obtained. The maximal size of an outbreak $n_{\ast }$ scales as $N^{2∕3}$ with $N$ the population size. This scaling law implies that the average outbreak size $⟨n⟩$ scales as $N^{1∕3}$. Moreover, the maximal and the average duration of an outbreak grow as $t_{\ast }\sim N^{1∕3}$ and $⟨t⟩\sim \text{ln}N$, respectively.