The stationary distribution in a stochastic SIS epidemic model with general nonlinear incidence

In this paper, a stochastic SIS type epidemic model with general nonlinear incidence is investigated. The diffusion process in the model is indicated to be degenerate. A new technique is proposed to investigate the existence of stationary distribution. By using the theory of integral Markov semigroup, the threshold criterion is established to ensure the existence of unique stationary distribution for the model. The numerical examples are carried out to illustrate our theoretical results.