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Solution of an infection model near threshold

David A. Kessler·Nadav M. Shnerb
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Abstract

We study the Susceptible-Infected-Recovered model of epidemics in the vicinity of the threshold infectivity. We derive the distribution of total outbreak size in the limit of large population size $N$. This is accomplished by mapping the problem to the first passage time of a random walker subject to a drift that increases linearly with time. We recover the scaling results of Ben-Naim and Krapivsky that the effective maximal size of the outbreak scales as $N^{2/3}$, with the average scaling as $N^{1/3}$, with an explicit form for the scaling function.

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David A. Kessler, Nadav M. Shnerb. 2007-01-17. Solution of an infection model near threshold. https://doi.org/10.1103/physreve.76.010901

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