Critical scaling of stochastic epidemic models

Details Critical scaling of stochastic epidemic models Critical scaling of stochastic epidemic models

2007-09-07

arxiv.org/abs/0709.1039v1

IMS Lecture Notes Monograph Series 2007, Vol. 55, 167-178

Mathematics

Probability

Published at http://dx.doi.org/10.1214/074921707000000346 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921707000000346

In the simple mean-field SIS and SIR epidemic models, infection is transmitted from infectious to susceptible members of a finite population by independent $p-$coin tosses. Spatial variants of these models are proposed, in which finite populations of size $N$ are situated at the sites of a lattice and infectious contacts are limited to individuals at neighboring sites. Scaling laws for both the mean-field and spatial models are given when the infection parameter $p$ is such that the epidemics are critical. It is shown that in all cases there is a critical threshold for the numbers initially infected: below the threshold, the epidemic evolves in essentially the same manner as its branching envelope, but at the threshold evolves like a branching process with a size-dependent drift.

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