Stochastic amplification in an epidemic model with seasonal forcing

Details Stochastic amplification in an epidemic model with seasonal forcing Stochastic amplification in an epidemic model with seasonal forcing

2010-05-13

arxiv.org/abs/1005.2372v2

J. Theor. Biol., 267, 85-94, (2010)

Biology

Quantitative Biology

Populations and Evolution

Updated with revisions and two new appendices

Scientific paper

10.1016/j.jtbi.2010.08.014

We study the stochastic susceptible-infected-recovered (SIR) model with time-dependent forcing using analytic techniques which allow us to disentangle the interaction of stochasticity and external forcing. The model is formulated as a continuous time Markov process, which is decomposed into a deterministic dynamics together with stochastic corrections, by using an expansion in inverse system size. The forcing induces a limit cycle in the deterministic dynamics, and a complete analysis of the fluctuations about this time-dependent solution is given. This analysis is applied when the limit cycle is annual, and after a period-doubling when it is biennial. The comprehensive nature of our approach allows us to give a coherent picture of the dynamics which unifies past work, but which also provides a systematic method for predicting the periods of oscillations seen in whooping cough and measles epidemics.

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