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


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.


Air pollution Stochastic differential equation Change point Respiratory infection Intervention measures 


  1. Aguilera I, Pedersen M, Garcia-Esteban R, Ballester F, Basterrechea M, Esplugues A, Fernández-Somoano A, Lertxundi A, Tardón A, Sunyer J (2013) Early-life exposure to outdoor air pollution and respiratory health, ear infections, and eczema in infants from the INMA study. Environ Health Perspect 121(3):387–392CrossRefGoogle Scholar
  2. Allen LJS, Allen EJ, Jonsson CB (2006) The impact of environmental variation on hantavirus infection in rodents. In: Gumel AB, Castillo-Chavez C, Mickens RE, Clemence DP (eds) Contemporary mathematics series. Proceedings of the joint summer research conference on modeling the dynamics of human diseases: emerging paradigms and challenges, vol 410. AMS, Providence, pp 1–15Google Scholar
  3. Becker S, Dailey LA, Soukup JM, Grambow S, Devlin RB, Huang YT (2005) Seasonal variations in air pollution particle-induced inflammatory mediator release and oxidative stress. Environ Health Perspect 113(8):1032–1038CrossRefGoogle Scholar
  4. Bernstein JA, Alexis N, Barnes C, Bernstein IL, Nel A, Peden D, Diaz-Sanchez D, Tarlo SM, Williams PB (2004) Health effects of air pollution. J Allergy Asthma Clin Immunol 114:116–1123Google Scholar
  5. Bing Z, Wilson E, Jun B (2011) Controlling air pollution from coal power plants in China: incremental change or a great leap forward. Environ Sci Technol 45(24):10294–5CrossRefGoogle Scholar
  6. Botchev MA, Verwer JG (2003) A new approximate matrix factorization for implicit time integration in air pollution modeling. J Comput Appl Math 157:309–327MathSciNetCrossRefGoogle Scholar
  7. Chan-Yeung MNW (2000) Air pollution and health. Hong Kong Med J 6:390–8Google Scholar
  8. Chauhan AJ, Johnston SL (2003) Air pollution and infection in respiratory illness. Br Med Bull 68:95–112CrossRefGoogle Scholar
  9. Chen BH, Kan HD, Chen RJ, Jiang SH, Hong CJ (2011) Air pollution and health studies in China-policy implications. J Air Waste Manag Assoc 61(11):1292–1299CrossRefGoogle Scholar
  10. Chen RJ, Zhang YH, Yang CX, Zhao ZH, Xu XH, Kan HD (2013) Acute effect of ambient air pollution on stroke mortality in the China air pollution and health effects study. Stroke 44:954–960CrossRefGoogle Scholar
  11. Chin JC, Broemeling LD (1980) Some Bayesian inferences for a changing linear model. Technometrics 22:71–78MathSciNetCrossRefGoogle Scholar
  12. Chow JC, Watson JG, Mauderly JL, Costa DL, Wyzga RE, Vedal S, Hidy GM, Altshuler Sam L, Marrack D, Heuss JM, Wolff GT, Pope CA, Dockery DW (2006) Health effects of fine particulate air pollution: lines that connect. J Air Waste Manag 56(10):1368–1378CrossRefGoogle Scholar
  13. Cropper M (2010) What are the health effects of air pollution in China? In: Heal G (ed) Is economic growth sustainable?. Palgrave-Macmillan, LondonGoogle Scholar
  14. Genc DD, Yesilyurt C, Tuncel G (2010) Air pollution forecasting in Ankara, Turkey using air pollution index and its relation to assimilative capacity of the atmosphere. Environ Monit Assess 166:11–27CrossRefGoogle Scholar
  15. HEI-International Scientific Oversight Committee (2010) Outdoor air pollution and health in the developing countries of Asia: a comprehensive review. Special Report 18. Health Effects Institute, BostonGoogle Scholar
  16. Huang L, Zhou L, Chen J, Chen K, Liu Y, Chen XD, Tang FY (2016) Acute effects of air pollution on influenza-like illness in Nanjing, China: a population-based study. Chemosphere 147:180–187CrossRefGoogle Scholar
  17. Ji Y (2014) Economic, growth, urbanization and air pollution in China: an empirical research based on panel data. Energies 7(7):4202–4220CrossRefGoogle Scholar
  18. Kampa M, Castanas E (2008) Human health effects of air pollution. Environ Pollut 151:362–367CrossRefGoogle Scholar
  19. Katsouyanni K (2003) Ambient air pollution and health. Br Med Bull 68:143–156CrossRefGoogle Scholar
  20. Kou SC, Kou SG (2004) A diffusion model for growth stocks. Math Method Oper Res 29:191–212MathSciNetCrossRefGoogle Scholar
  21. Li FZ, Liu Y, Lü JJ, Liang LC, Harmer P (2015) Ambient air pollution in China poses a multifaceted health threat to outdoor physical activity. J Epidemiol Commun 69(3):201–204CrossRefGoogle Scholar
  22. Low RB, Bielory L, Qureshi AI, Dunn V, Stuhlmiller DFE, Dickey DA (2006) The relation of stroke admissions to recent weather, airborne allergens, air pollution, seasons, upper respiratory infections, and asthma incidence, September 11, 2001, and day of the week. Stroke 37:951–957CrossRefGoogle Scholar
  23. Lyons TJ, Zheng WA (1990) On conditional diffusion processes. Proc R Soc Edinb Sect A 115:243–255MathSciNetCrossRefGoogle Scholar
  24. Mehta S, Shin H, Burnett R, North T, Cohen AJ (2013) Ambient particulate air pollution and acute lower respiratory infections: a systematic review and implications for estimating the global burden of disease. Air Qual Atmos Health 6:69–83CrossRefGoogle Scholar
  25. Mostofsky E, Schwartz J, Coull BA, Koutrakis P, Wellenius GA, Suh HH, Gold DR, Mittleman MA (2012) Modeling the association between particle constituents of air pollution and health outcomes. Am J Epidemiol 176(4):317–C326CrossRefGoogle Scholar
  26. Nielsen CP, Ho MS (2007) Air pollution and health damages in China: an introduction and review. In: Ho MS, Nielsen CP (eds) Clearing the air: the health and economic damages of air pollution in China. MIT Press, CambridgeGoogle Scholar
  27. Peng RD, Dominici F, Pastor-Barriuso R, Zeger SL, Samet JM (2005) Seasonal analyses of air pollution and mortality in 100 US cities. Am J Epidemiol 161:585–594CrossRefGoogle Scholar
  28. Poon JPH, Casas I, He CF (2006) The impact of energy, transport, and trade on air pollution in China Eurasian geography and economics. Eurasian Geogr Econ 47(5):568–584CrossRefGoogle Scholar
  29. Raaschou-Nielsen O, Andersen ZJ, Beelen R, Samoli E, Stafoggia M (2013) Air pollution and lung cancer incidence in 17 European cohorts: prospective analyses from the European Study of Cohorts for Air Pollution Effects (ESCAPE). Lancet Oncol 14(9):813CrossRefGoogle Scholar
  30. Rohde RA, Muller RA (2015) Air pollution in China: mapping of concentrations and sources. PLoS ONE 10(8):e0135749CrossRefGoogle Scholar
  31. Samoli E, Schwartz J, Wojtyniak B, Touloumi G, Spix C, Balducci F, Medina S, Rossi G, Sunyer J, Bacharova L, Anderson HR, Katsouyanni K (2001) Investigating regional differences in short-term effects of air pollution on daily mortality in the APHEA Project: a sensitivity analysis for controlling long-term trends and seasonality. Stoch Environ Res Risk Assess 109(4):349–353Google Scholar
  32. Shostya A (2016) Ambient air pollution in China: predicting a turning point. Int Adv Econ Res 22:295–307CrossRefGoogle Scholar
  33. Song CB, Wu L, Xie YC, He JJ, Chen X, Wang T, Lin YC, Jin TS, Wang AX, Liu Y, Dai QL, Liu BS, Wang YN, Mao HJ (2017) Air pollution in China: status and spatiotemporal variations. Environ Pollut 227:334–347CrossRefGoogle Scholar
  34. Stern G, Latzin P, Röösli M, Fuchs O, Proietti E, Kuehni C, Frey U (2013) A prospective study of the impact of air pollution on respiratory symptoms and infections in infants. Am J Respir Crit Care Med 187(12):1341–1348CrossRefGoogle Scholar
  35. Sun CW, Yuan X, Yao X (2016) Social acceptance towards the air pollution in China: evidence from public’s willingness to pay for smog mitigation. Energy Policy 92:313–324CrossRefGoogle Scholar
  36. Tang SY, Heron EA (2008) Bayesian inference for a stochastic logistic model with switching points. Ecol Model 219:153–169CrossRefGoogle Scholar
  37. Tang SY, Xiao YN, Yang YP, Zhou YC, Wu JH, Ma ZE (2010) Community-based measures for mitigating the 2009 H1N1 pandemic in China. PLoS ONE 5:e10911CrossRefGoogle Scholar
  38. Tang SY, Yan QL, Shi W, Wang X, Sun XD, Yu PB, Wu JH, Xiao YN (2018) Measuring the impact of air pollution on respiratory infection risk in China. Environ Pollut 232:477–486CrossRefGoogle Scholar
  39. Touloumi G, Samoli E, Pipikou M, Tertre AL, Atkinson R, Katsouyanni K (2006) Seasonal confounding in air pollution and health time-series studies: effect on air pollution effect estimates. Stat Med 25:4164–4178MathSciNetCrossRefGoogle Scholar
  40. Wang XK, Lu WZ (2006) Seasonal variation of air pollution index: Hong Kong case study. Chemosphere 63:1261–1272CrossRefGoogle Scholar
  41. Xia XL, Zhang A, Liang S, Qi QW, Jiang L, Ye YJ (2017) The association between air pollution and population health risk for respiratory infection: a case study of Shenzhen, China. Int J Environ Res Public Health 14(9):950CrossRefGoogle Scholar
  42. Xiao QY, Ma ZW, Li SS, Liu Y (2015) The impact of winter heating on air pollution in China. PLoS ONE 10(1):e0117311CrossRefGoogle Scholar
  43. Yu B, Huang CM, Liu ZH, Wang HP, Wang LL (2011) A chaotic analysis on air pollution index change over past 10 years in Lanzhou, northwest China. Stoch Environ Res Risk Assess 25:643–653CrossRefGoogle Scholar
  44. Zhao Y, Wang SX, Duan L, Lei Y, Cao PF, Hao JM (2008) Primary air pollutant emissions of coal-fired power plants in China: current status and future prediction. Atmos Environ 42:8442–8452CrossRefGoogle Scholar
  45. Zhang JF, Smith KR (2007) Household air pollution from coal and biomass fuels in China: measurements, health impacts, and interventions. Environ Health Perspect 115(6):848–855CrossRefGoogle Scholar

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

Personalised recommendations