Analysis of a stochastic SIB cholera model with saturation recovery rate and Ornstein-Uhlenbeck process

In this paper, a stochastic SIB(Susceptible-Infected-Vibrios) cholera model with saturation recovery rate and Ornstein-Uhlenbeck process is investigated. It is proved that there is a unique global solution for any initial value of the model. Furthermore, the sufficient criterion of the stationary distribution of the model is obtained by constructing a suitable Lyapunov function, and the expression of probability density function is calculated by the same condition. The correctness of the theoretical results is verified by numerical simulation, and the specific expression of the marginal probability density function is obtained.