Journal
JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
Volume -, Issue -, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1742-5468/2011/12/P12006
Keywords
stochastic processes (theory); epidemic modelling
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Funding
- EPSRC
- Australian Research Council's Discovery Projects [DP110102893]
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We calculate both the exponential and prefactor 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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