Abstract
Abstract: Since the beginning of 2020 the world has been facing the largest virological invasion in the form. of the COVID-19 pandemic, and the outbreak of COVID-19 has once again demonstrated that infectious diseases remain one of the greatest threats to human survival and development. In this paper, therefore, the existence of a stationary distribution for a class of stochastic COVID-19 infectious disease SEIW (W is the concentration of virus in the environment) models that take into account the effect of environmental viruses is investigated. First, the existence and uniqueness of the solution of the system are proved by constructing a suitable Lyapunov function. The parameters Rs0 are then established using the stochastic Lyapunov method and the existence of a unique stationary distribution of the system solution on R4+ when Rs0 >1 is demonstrated. And by comparing the deterministic model of R0 and the stochastic model of Rs0 , it can be found that Rs0 is influenced by white noise and Rs0 ≤R0, when σi →0 (i=1, 2, 3, 4) , Rs0 →R0, indicating that the work in this paper is an extension of the deterministic model and when the random perturbations are small, there exists a unique stationary distribution on R4+ for the system solution.
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