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Study on a Stochastic Avian Influenza Epidemic Model with Generalized Incidence Rate

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Document pages: 18 pages

Abstract: Avian Influenza, with ahigh mortality rate in human population, is considered to be one of the mostsignificant potential threats to human beings. Based on a recent avianinfluenza SI-SIR model with logistic growth for birds, we propose a stochasticmodel with generalized incidence rate. For the stochastic avian-only system,sufficient conditions for the extinction of infected birds are established, andthe existence of a unique ergodic stationary distribution is also obtained. Forthe stochastic avian-human system, a threshold number is established, andhence the extinction of disease is investigated. From the viewpoint of biology,the noise intensity in the infected birds playsa key role in the evolutionary dynamics. Moreover, we also analyze theasymptotic behavior around the endemic equilibrium of the correspondingdeterministic model.

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