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Bulletin of Mathematical Biology

, Volume 80, Issue 12, pp 3127–3153 | Cite as

Stochastic Modelling of Air Pollution Impacts on Respiratory Infection Risk

  • Sha He
  • Sanyi TangEmail author
  • Yanni Xiao
  • Robert A. Cheke
Original Article

Abstract

The impact of air pollution on people’s health and daily activities in China has recently aroused much attention. By using stochastic differential equations, variation in a 6 year long time series of air quality index (AQI) data, gathered from air quality monitoring sites in Xi’an from 15 November 2010 to 14 November 2016 was studied. Every year the extent of air pollution shifts from being serious to not so serious due to alterations in heat production systems. The distribution of such changes can be predicted by a Bayesian approach and the Gibbs sampler algorithm. The intervals between changes in a sequence indicate when the air pollution becomes increasingly serious. Also, the inflow rate of pollutants during the main pollution periods each year has an increasing trend. This study used a stochastic SEIS model associated with the AQI to explore the impact of air pollution on respiratory infections. Good fits to both the AQI data and the numbers of influenza-like illness cases were obtained by stochastic numerical simulation of the model. Based on the model’s dynamics, the AQI time series and the daily number of respiratory infection cases under various government intervention measures and human protection strategies were forecasted. The AQI data in the last 15 months verified that government interventions on vehicles are effective in controlling air pollution, thus providing numerical support for policy formulation to address the haze crisis.

Keywords

Air pollution Stochastic differential equation Change point Respiratory infection Intervention measures 

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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  • Sha He
    • 1
  • Sanyi Tang
    • 1
    Email author
  • Yanni Xiao
    • 2
  • Robert A. Cheke
    • 3
  1. 1.School of Mathematics and Information ScienceShaanxi Normal UniversityXi’anPeople’s Republic of China
  2. 2.School of Mathematics and StatisticsXi’an Jiaotong UniversityXi’anPeople’s Republic of China
  3. 3.Natural Resources InstituteUniversity of Greenwich at MedwayChathamUK

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