A stochastic SIS model driven by random diffusion of air pollutants

Sha He, Sanyi Tang and Weiming Wang

Physica A: Statistical Mechanics and its Applications, 2019, vol. 532, issue C

Abstract: 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.

Keywords: Air pollution; Respiratory disease; Stochastic SIS model; Noise intensity; Uncertainty and sensitivity analysis (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (6)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:532:y:2019:i:c:s0378437119310064

DOI: 10.1016/j.physa.2019.121759

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