Abstract: Based on the fact that epidemics are affected by environmental noise and psychological effects, a stochastic SIRS epidemic model with Logistic growth and psychological effects is established to discuss the effects of Logistic growth and psychological effects on the global dynamics of the model. Firstly, by constructing the Lyapunov function and using the It$\hat{\rm o}$ formula, the existence and uniqueness of the global positive solution of the model are proved, and then, under appropriate conditions, by using the random Lyapunov function method, the sufficient conditions for the existence of ergodic stationary distribution of the positive solution of the model are obtained by using the LaSalle invariance principle. The results show that environmental and psychological change can inhibit the disease under certain conditions. Finally, the correctness of the theoretical results is verified by numerical simulation.

Key words: SIRS epidemic model, Logistic growth, psychology effect, stationary distribution, ergodicity