A stochastic SEIRS rabies model with population dispersal: Stationary distribution and probability density function

Abstract

In this paper, we propose a stochastic SEIRS rabies epidemic models with two patches to investigate the spatial spread of rabies under the influence of environmental noise. Adopting a new technique to construct the stochastic Lyapunov functions, we obtain the sufficient conditions for the existence of an ergodic stationary distribution. In addition, if the movement of dogs is forbidden, we obtain the exact expression of probability density function around a quasi-equilibrium point. Finally, numerical simulations are employed to verify our analytical results and reveal the impact of stochastic perturbations on rabies transmission.