Dynamic analysis and optimal control of a stochastic COVID-19 model

Abstract

In this paper, we construct a stochastic SAIR (Susceptible–Asymptomatic–Infected–Removed) epidemic model to study the dynamic and control strategy of COVID-19. The existence and uniqueness of the global positive solution are obtained by using the Lyapunov method. We prove the necessary conditions for the existence of extinction and ergodic stationary distribution by defining two new thresholds, respectively. Through the stochastic control theory, the optimal control strategy is obtained. Numerical simulations show the validity of stationary distribution and optimal control. The parameters of the model are estimated by a set of real COVID-19 data. And, the sensitivity of all parameters shows that decreasing physical interaction and screening the asymptomatic as swiftly as possible can prevent the wide spread of the virus in communities. Finally, we also display the trend of the epidemic without control strategies.