Stationary distribution and probability density for a stochastic SEIR-type model of coronavirus (COVID-19) with asymptomatic carriers

In this paper, we propose a stochastic SEIR-type model with asymptomatic carriers to describe the propagation mechanism of coronavirus (COVID-19) in the population. Firstly, we show that there exists a unique global positive solution of the stochastic system with any positive initial value. Then we adopt a stochastic Lyapunov function method to establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of positive solutions to the stochastic model. Especially, under the same conditions as the existence of a stationary distribution, we obtain the specific form of the probability density around the quasi-endemic equilibrium of the stochastic system. Finally, numerical simulations are introduced to validate the theoretical findings.