Abstract
•A stochastic cholera model between communities linked by migration is studied.•We obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution.•Our result shows that the migration and the small white noise are not beneficial for eliminating cholera.•Some examples together with numerical simulations are introduced to support the theoretical result.
In this paper, we develop and study a stochastic cholera model between communities linked by migration. Firstly, we show that there exists a unique global positive solution of the considered system with any positive initial value. Then by using the stochastic Lyapunov analysis method, we obtain sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model. Our result shows that the migration and the small white noise are not beneficial for eliminating cholera. Finally, some examples together with numerical simulations are introduced to support the theoretical result.