Dynamical behavior and optimal control of a stochastic mathematical model for cholera

A stochastic cholera model with saturation recovery rate is discussed. Firstly, the existence and uniqueness of the global positive solution of the system are proved. Secondly, the asymptotic behavior of the solutions of the stochastic cholera model near the disease-free equilibrium and the corresponding deterministic endemic equilibrium is discussed. Then, the phenomenon that the large noise can cause the extinction of cholera is obtained. Furthermore, on the basis of the stochastic model, the optimal control is added and studied to provide a theoretical basis for the prevention and control of cholera. Finally, the theoretical results are verified by numerical simulations and some suggestions on how to better control the disease are presented.