WKB calculation of an epidemic outbreak distribution

Details WKB calculation of an epidemic outbreak distribution WKB calculation of an epidemic outbreak distribution

2011-10-24

arxiv.org/abs/1110.5375v2

J. Stat. Mech. (2011) P12006

Biology

Quantitative Biology

Populations and Evolution

Updated with some minor corrections

Scientific paper

10.1088/1742-5468/2011/12/P12006

We calculate both the exponential and pre-factor contributions in a WKB approximation of the master equation for a stochastic SIR model with highly oscillatory dynamics. Fixing the basic parameters of the model we investigate how the outbreak distribution changes with the population size. We show that this distribution rapidly becomes highly non-Gaussian, acquiring large tails indicating the presence of rare, but large outbreaks, as the population is made smaller. The analytic results are found to be in excellent agreement with simulations until the systems become so small that the dynamics are dominated by fade-out of the disease.

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