Stationary distribution of a stochastic cholera epidemic model with vaccination under regime switching

This paper is concerned with a stochastic cholera epidemic model with vaccination, which is perturbed by both white noise and colored noise. For this stochastic model, we derive an important condition R0s which depends on environmental noises. Through constructing suitable Lyapunov function, we obtain that this model admits a unique ergodic stationary distribution if R0s>1. Results show that when white noise is small, the stochastic system has a stochastic positive equilibrium state without changing the essential properties of the corresponding deterministic system.