Asymptotic Behavior Of A Stochastic Epidemic Model With Saturatied Incidence

In the paper,we study a class of nonlinear stochastic SIR model(3).Our model has two random perturbations in this way of randomizing the disease transmission coefficient and removal rates,which is different from a general stochastic model.We prove that a globally positive solution of the nonlinear SDE is existent and unique.We discuss the extinction and persistence of the disease by new stochastic Lyapunov functions.In the case of extinction,the susceptible component weakly to an inverse-Gamma distribution when the infective component is extinct.In the case of persistence,we get a sufficient condition the ergodic property and positive recurrence of the SDE's solution.Furthermore,we obtain a representation of mean of the SDE's stationary distribution.