A note on the stationary distribution of stochastic SIS epidemic model with vaccination under regime switching

In this paper, the stochastic SIS epidemic model with vaccination under regime switching is further investigated. A new threshold Rs 0 which is different from that given in [22] is established. A new technique to deal with the nonlinear incidence and vaccination for stochastic epidemic model under regime switching is proposed. When Rs0 > 0, the existence of a unique stationary distribution and the ergodic property are obtained by constructing a new stochastic Lyapunov function with Markov switching. The corresponding result which is acquired in [22] is improved and extended.