Dynamics of a stochastic rabies epidemic model with Markovian switching

In this paper,we analyze a stochastic rabies epidemic model which is perturbed by both white noise and telegraph noise.First,we prove the existence of the unique global positive solution.Second,by constructing an appropriate Lyapunov function,we establish a sufficient condition for the existence of a unique ergodic stationary distribution of the positive solutions to the model.Then we establish sufficient conditions for the extinction of diseases.Finally,numerical simulations are introduced to illustrate our theoretical results.