Abstract
•A stochastic dengue epidemic model is proposed and studied.•We obtain sufficient conditions for the existence of an ergodic stationary distribution to the model.•We establish sufficient conditions for extinction of the diseases.•The existence of stationary distribution implies stochastic weak stability.
In this paper, we investigate the dynamical behavior of a stochastic dengue epidemic model. First of all, by constructing a suitable stochastic Lyapunov function, we obtain sufficient conditions for the existence of an ergodic stationary distribution of the positive solutions to the model. Then we establish sufficient conditions for extinction of the diseases. The existence of stationary distribution implies stochastic weak stability.