Stochastic epidemic dynamics based on the association between susceptible and recovered individuals

In this paper,we propose a new mathematical model based on the association between susceptible and recovered individual.Then,we study the stability of this model with the deterministic case and obtain the conditions for the extinction of diseases.Moreover,in view of the association between susceptible and recovered individual perturbed by white noise,we also give sufficient conditions for the extinction and the permanence in mean of disease with the white noise.Finally,we have numerical simulations to demonstrate the correctness of obtained theoretical results.