The Stationary Distribution and Extinction of a Stochastic Five‐Dimensional COVID‐19 Model

Abstract

This paper investigates a stochastic SEIAIR epidemic model with nonlinear incidence and contacting distance to describe the transmission dynamics of COVID‐19. Firstly, we show the global existence of positive solution of the system. Then, using the Lyapunov function method and theory of stochastic analysis, we set out the sufficient conditions of the existence and uniqueness of an ergodic stationary distribution to the stochastic model. Furthermore, we obtain the sufficient condition for extinction of the disease. Finally, we go through some numerical simulations to demonstrate the theoretical results. Our study extends and improves the results of previous studies.