Abstract
•A stochastic SEI epidemic model with general distributed delay is established.•The existence of a unique global positive solution for the stochastic model are proved.•We prove that there is a stationary solution to the stochastic system.•Two probability density functions with respect to the stationary solution are obtained.•Some sufficient conditions are established for the disease extinction of stochastic system.
A stochastic SEI (Susceptible-Exposed-Infected) epidemic model with general distributed delay is studied in this paper. First, we prove the existence and uniqueness of a global positive solution to the stochastic system. By means of the Lyapunov method, we verify the existence of a stationary distribution of the positive solution under a stochastic criterion R0p>1, which is known as stationary solution. Moreover, if R0p>1, two exact probability density functions around the quasi-stable equilibrium are obtained by solving the corresponding Fokker-Planck equation. Notably, both the explicit expression of density function and the existence of stationary distribution suggest the disease persistence in biological sense. For completeness, some sufficient conditions for disease extinction are established. At last, several numerical simulations are provided to verify our analytical results and reveal the impact of stochastic perturbations on disease transmission.