A stochastic epidemic model coupled with seasonal air pollution: analysis and data fitting

Abstract

Air pollution increases the risk of getting respiratory diseases. Both the removal of air pollutants and the transmission of diseases can be influenced by random perturbations. In this work, we develop a stochastic differential equation (SDE) model, coupled with seasonal air pollution, to study the dynamics of infectious respiratory disease spread. The periodicity of disease outbreaks is assumed to be caused by seasonal air pollution. The SDE of the air quality index (AQI) is proved to be ultimately bounded. The complexity of the SDE of infected individuals lies in the transmission rate that depends on air pollution. We prove that the system driven by the periodic clearance rate has at least one stochastic periodic solution under certain conditions. By computing the closed form of the Hermite expansion of transformation density, we construct an approximate likelihood function to fit the data of AQI and influenza-like illness cases, as a case study. Data fitting shows that the stochastic periodic model can well capture the dynamical behavior of air pollution and outbreaks of the infectious respiratory disease. We also study the impact of parameters on the reduction of air pollution and disease spread. This work shows the correlation between air pollution and infectious respiratory disease outbreaks and illustrates that the intensity of the environmental disturbance is a factor that cannot be ignored.