Estimation of the Dynamics of Coronavirus Infection by Stochastic Infectious Disease Biological System

ABSTRACT The pneumonia caused by coronavirus infection seriously threatens the lives and health of the people and is a war without fire. The paper considers the COVID‐19 model with susceptible, latent, asymptomatic, symptomatic, and rehabilitative stages. First, we study the local stability of boundary equilibrium points for deterministic systems. Then, the model is dimensionally reduced by a limit set, and the method of Lyapunov functions is used to prove that the endemic equilibrium point is locally asymptotically stable for the dimensionally reduced model. For stochastic systems with Ornstein–Uhlenbeck processes, we first prove the existence and uniqueness of positive solution. In addition, in‐depth research was conducted on the persistence and extinction of the disease. And the density function near the positive equilibrium point is described in detail. Finally, some numerical simulations help us verify the above conclusions.