Stationary solution, extinction and density function for a high-dimensional stochastic SEI epidemic model with general distributed delay

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 pos-itive 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 R-0(p) > 1 , which is known as stationary solution. Moreover, if R-0(p) > 1 , two exact probability density functions around the quasi-stable equilibrium are obtained by solving the corre-sponding 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 re-veal the impact of stochastic perturbations on disease transmission. (C) 2021 Elsevier Inc. All rights reserved.

Automated summary

This paper studies a stochastic SEI epidemic model with general distributed delay, proving the existence and uniqueness of a global positive solution and verifying the existence of a stationary distribution under a stochastic criterion. The study also obtains exact probability density functions around the quasi-stable equilibrium and establishes conditions for disease extinction. Numerical simulations are provided to reveal the impact of stochastic perturbations on disease transmission.