Dynamics for a class of stochastic SIS epidemic models with nonlinear incidence and periodic coefficients

In this paper, we investigate the dynamics of a class of periodic stochastic SIS epidemic models with general nonlinear incidence f(S,I). Some sufficient conditions on the permanence in the mean and extinction of positive solutions with probability one are established. By using the Khasminskii's boundary periodic Markov processes, the existence of stochastic nontrivial periodic solution for the models is also obtained. The numerical simulations are given to illustrate the main theoretical results and some interesting conjectures are presented.