Abstract
Abstract An SEIR epidemic model with constant immigration and random fluctuation around the endemic equilibrium is considered. As a special case, a deterministic system discussed by Li et al. will be incorporated into the stochastic version given by us. We carry out a detailed analysis on the asymptotic behavior of the stochastic model, also regarding of the basic reproduction number ℛ0. By means of Lyapunov functions we give sufficient conditions for globally stochastically asymptotic stability of the unique positive endemic equilibrium. When ℛ0 > 1, under the sufficient conditions, we deduce the globally asymptotic stability of the endemic equilibrium by measuring the difference between the solution and the endemic equilibrium of the deterministic model in time average, the disease will prevail and the infected fraction persists. Numerical simulations support our analytical conclusions and show the effect of intensity of white noise on stability of the system.
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