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Abstract: We study the stochastic susceptible-infected-recovered SIR model withtime-dependent forcing using analytic techniques which allow us to disentanglethe interaction of stochasticity and external forcing. The model is formulatedas a continuous time Markov process, which is decomposed into a deterministicdynamics together with stochastic corrections, by using an expansion in inversesystem size. The forcing induces a limit cycle in the deterministic dynamics,and a complete analysis of the fluctuations about this time-dependent solutionis given. This analysis is applied when the limit cycle is annual, and after aperiod-doubling when it is biennial. The comprehensive nature of our approachallows us to give a coherent picture of the dynamics which unifies past work,but which also provides a systematic method for predicting the periods ofoscillations seen in whooping cough and measles epidemics.



Autor: Andrew J Black, Alan J McKane

Fuente: https://arxiv.org/







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