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Moderate deviations and extinction of an epidemic. (English) Zbl 1445.60022

Summary: Consider an epidemic model with a constant flux of susceptibles, in a situation where the corresponding deterministic epidemic model has a unique stable endemic equilibrium. For the associated stochastic model, whose law of large numbers limit is the deterministic model, the disease free equilibrium is an absorbing state, which is reached soon or later by the process. However, for a large population size, i.e. when the stochastic model is close to its deterministic limit, the time needed for the stochastic perturbations to stop the epidemic may be enormous. In this paper, we discuss how the central limit theorem, moderate and large deviations allow us to give estimates of the extinction time of the epidemic.

MSC:

60F05 Central limit and other weak theorems
60F10 Large deviations
92D30 Epidemiology
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References:

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