A Stochastic Epidemic Model with Constant Immigration and Multi-Dimensional Noises

In this paper we extend a classical SIS epidemic model from a deterministic framework to a stochastic one by introducing two random perturbations in the model for transmission parameter and cure parameter, and formulate it as stochastic differential equation (SDE) for the number of infectious individuals (t). Then we prove that this SDE has a unique global positive solution and establish conditions for extinction. So it is clear that the basic reproductive number R P for the deterministic SIS model is larger than the basic reproductive number R for the SDE model, which means for the sake of extinction of 1(t), the condition of stochastic SIS model may be weaker than that of the deterministic SIS model. The results are illustrated by computer simulations.