Analysis of a Stochastic Susceptible-Infective Epidemic Model in a Polluted Atmospheric Environment

Atmospheric pollution is deteriorating, which has affected the evolution of respiratory disease for the exposed human worldwide. Thus, exploring the influence of air pollution on the evolution of disease transmission dynamics is a significant issue. In this article, a stochastic susceptible-infective (SI) epidemic model in a polluted atmospheric environment is investigated. The existence and uniqueness of the global positive solution are established. In virtue of the aggregation methods and Lyapunov function, the sufficient conditions of disease extinction, persistence, and existence of the stationary distribution are established, respectively. Taking PM2.5 concentration as the air pollutant index, numerical simulations are carried out to support these results. Our results indicated that the disease transmission dynamics (extinction, persistence, and stationary distribution) are significantly associated with the environmental atmospheric pollution and fluctuation.