Dynamics of a stochastic SEIAIR COVID-19 model with contacting distance and Ornstein-Uhlenbeck process

In this paper, a stochastic SEIAIR COVID-19 model with contacting distance and Ornstein-Uhlenbeck process is investigated to examine the influence of stochastic perturbation. The existence of unique global solution with any positive initial condition is first obtained. Then, the new threshold values R-0(e) and R-0(s) for the stochastic model are defined. When R-0(e)<1 the almost surely exponential extinction of disease is obtained. When R-0(s)>1 the existence of a unique stationary distribution is established by constructing the suitable Lyapunov function. Furthermore, the normal density function of stationary solution is calculated by using the calculation method of Lyapunov matrix equation. The numerical simulations are given to confirm the theoretical results. The specific expression of the marginal probability density function is obtained. By analyzing the threshold value R-0(s), we can conclude that contact distance has an important impact on disease transmission for deterministic models, but contact distance may lose its role in disease transmission for stochastic models due to the influence of randomness.