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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