The asymptotic behaviours of an epidemic model with two correlated stochastic perturbations

This paper mainly discussed the asymptotic dynamics of stochastic SI epidemic model and its improved model. Taking two stochastic disturbances into account in the deterministic model, in the form of Gaussian white noises, we obtained its invariant probability distribution by applying Fokker–Planck equation. We mainly focuses on the influence of the size of the correlation coefficient of two stochastic perturbations on stochastic epidemic model, under two stochastic disturbance, the correlative of two stochastic disturbances can affect the dynamics of the epidemic model, and the effects are different if we introduce the stochastic disturbance in different ways.