Persistence in a Stochastic SEIR Model with Constant Immigration in Incubation Period

A kind of stochastic susceptible-exposed but not infectiousinfectious-removed （SEIR） model with constant immigration in incubation period is presented, based on a deterministic SEIR model, via the technique of parameter perturbation which is standard in stochastic population modeling. The influence of the environmental noise as a standard Gaussian white noise on the epidemics＇ transmission is studied. Furthermore,the condition for the epidemics＇ persistence is obtained by formulating the corresponding function and using It ＇s formula. And the asymptotic behavior of the model near the endemic disease equilibrium is also studied. In this way, the decision support is provided in the application of this kind of stochastic SEIR model on the epidemics＇ prevention and control.