The threshold of a stochastic Susceptible–Infective epidemic model under regime switching

• A stochastic SI epidemic model under regime switching is proposed and investigated.
• We establish sufficient conditions for the existence of a unique ergodic stationary distribution.
• We obtain the threshold which ensures the extinction and the existence of the stationary distribution of the epidemic.

In this paper, we consider a stochastic Susceptible–Infective (SI) epidemic model under regime switching. Firstly, by constructing suitable Lyapunov functions, we establish sufficient criteria for the existence and uniqueness of an ergodic stationary distribution. Then we obtain the threshold which guarantees the extinction and the existence of the stationary distribution of the epidemic. Finally, some numerical simulations are introduced to illustrate our main results.