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

Abstract 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.

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