A stochastic SIS model driven by random diffusion of air pollutants

In this paper, a stochastic SIS model related to respiratory disease driven by random diffusion of air pollutants has been developed, in which the transmission coefficient is a function of air quality index. By applying the statistical properties of stochastic process, we derive a one-dimensional stochastic differential equation (SDE) model for the number of infected individuals. Then we show the existence and uniqueness of positive solution of the SDE model. Moreover, the critical conditions that guarantee the persistence and extinction have been obtained, meanwhile the results reveal that strong noise intensity will make the disease extinct instead. In fact, we find that the random fluctuation of the original two-dimensional coupling model and the reduced model are different by comparing their sample paths. The corresponding images of power spectral densities related to real data and the two models further illustrate this phenomenon. Finally, uncertainty and sensitivity analyses reveal that the parameters related to air pollution have great influence on the critical condition and dynamics of the proposed model. • A stochastic SIS epidemic model driven by air pollution is proposed and studied. • Threshold condition for disease extinction and persistence is obtained. • Main results reveal that the strong noise intensity is benefit for disease control. • Power spectral densities and true data are employed to compare the dynamics. • Uncertainty and sensitivity analyses reveal the key parameters on disease spread.