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

Abstract

In this paper, we propose a stochastic SEIR-type model 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. spectively. S(t) denotes the number of individuals who are susceptible to the disease, E(t) represents the number of exposed (in the latent period) individuals and R(t) represents the number of individuals who have been infected and then removed from the possibility of being infected again at time t, respectively. All parameters are strictly positive and their descriptions are given in Table 1.