Size of Outbreaks Near the Epidemic Threshold

E. Ben-Naim and P.L. Krapivsky

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 $n_*$ scales as $N^{2/3}$ with $N$ the population size. This scaling law implies that the average outbreak size $\langle n\rangle$ scales as $N^{1/3}$. Moreover, the maximal and the average duration of an outbreak grow as $t_*\sim N^{1/3}$ and $\langle t\rangle\sim \ln N$, respectively.


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