Solution of an infection model near threshold

Details Solution of an infection model near threshold Solution of an infection model near threshold

2007-01-17

arxiv.org/abs/q-bio/0701024v1

Biology

Quantitative Biology

Populations and Evolution

Scientific paper

10.1103/PhysRevE.76.010901

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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