Microbial Risk Assessment for Drinking Water

  • Stephen E. Chick
  • Sada Soorapanth
  • James S. Koopman
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 70)


Infectious microbes can be transmitted through the drinking water supply. Recent research indicates that infection transmission dynamics influence the public health benefit of water treatment interventions, although some risk assessments currently in use do not fully account for those dynamics. This chapter models the public health benefit of two interventions: improvements to centralized water treatment facilities, and localized point-of-use treatments in the homes of particularly susceptible individuals. A sensitivity analysis indicates that the best option is not as obvious as that suggested by an analysis that ignores infection dynamics suggests. Deterministic and stochastic dynamic systems models prove to be useful tools for assessing the dynamics of risk exposure.

Key words

Microbial risk Epidemic model Water treatment Stochastic infection model Ornstein-Uhlenbeck process 


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  1. [1]
    Hoxie, N.J., J.P Davis, J.M Vergeront, R. Nashold, and K. Blair (1997). Cryptosporidiosis-associated mortality following a massive waterborne outbreak in Milwaukee, Wisconsin. American Journal of Public Health, 87, 2032–2035.PubMedCrossRefGoogle Scholar
  2. [2]
    MacKenzie, W.R., et al. (1994), A massive outbreak in Milwaukee of Cryptosporidium infection transmitted through the public water supply. New England Journal of Medicine, 331, 161–167.CrossRefGoogle Scholar
  3. [3]
    Iley, K. (2002). Aid groups urge action on water-borne diseases. Reuters News Service at, March 25.Google Scholar
  4. [4]
    Cowdy, H. (2002). Millions at risk from contaminated water. Reuters News Service at, March 25.Google Scholar
  5. [5]
    Centers for Disease Control and Prevention (2001). Norwalk-like viruses: Public health consequences and outbreak management. Morbidity and Mortality Weekly Report, 50(RR-9), 1–17.Google Scholar
  6. [6]
    Cooke, R. and B. Kraan (2000). Processing expert judgements in accident consequence modelling. Radiation Protection Dosimetry, 90, 311–315.Google Scholar
  7. [7]
    Stewart, M.H., M.V. Yates, M.A. Anderson, C.P. Gerba, J.B. Rose, R. DeLeon, and R.L. Wolfe (2002). Predicted public health consequences of body-contact recreation on a potable water reservoir. Journal of the American Water Works Association, 94, 84–97.Google Scholar
  8. [8]
    Stout, J.E., Y-S E. Lin, A.M. Goetz, and R.R. Muder (1998). Controlling legionella in hospital water systems: Experience with the superheat-and-flush method and copper-silver ionization. Infection Control and Hospital Epidemiology, 19, 663–674.CrossRefGoogle Scholar
  9. [9]
    Current, W. (1994). Cryptosporidium parvum: Household transmission. Annals of Internal Medicine, 120, 518–519.PubMedGoogle Scholar
  10. [10]
    Medema, G. and J. Schijven (2001). Modeling the sewage discharge and dispersion of Cryptosporidium and giardia in surface water. Water Research, 35, 4370–4316.CrossRefGoogle Scholar
  11. [11]
    Regli, S., J.B. Rose, C.N. Haas, and C.P. Gerba (1991). Modeling the risk from giardia and viruses in drinking water. Journal of the American Water Works Association, 83, 76–84.Google Scholar
  12. [12]
    International Life Sciences Institute (2000). Revised Framework for Microbial Risk Assessment. ILSI Risk Science Institute workshop report, International Life Sciences Institute, Washington, DC.Google Scholar
  13. [13]
    Eisenberg, J.E., E.Y.W. Seto, J.M. Colford Jr, A. Olivieri, and R.C. Spear (1998). An analysis of the Milwaukee Cryptosporidiosis outbreak based on a dynamic model of the infection process. Epidemiology, 9, 255–263.PubMedCrossRefGoogle Scholar
  14. [14]
    Chick, S.E., J.S. Koopman, S. Soorapanth, and M. E. Brown (2001). Infection transmission system models for microbial risk assessment. Science of the Total Environment, 274, 197–207.CrossRefPubMedGoogle Scholar
  15. [15]
    Frisby, H.R., D.G. Addiss, W.J. Reiser, et al. (1997). Clinical and epidemiologic features of a massive waterborne outbreak of WJ Cryptosporidiosis in persons with HIV infection. Journal of Acquired Immune Deficiency Syndromes and Human Retrovirology, 16, 367–373.PubMedGoogle Scholar
  16. [16]
    Chick, S.E., J.S. Koopman, S. Soorapanth, and B.K. Boutin (2003). Inferring infection transmission parameters that influence water treatment decisions. Management Science, 49, 920–935.CrossRefGoogle Scholar
  17. [17]
    Brookhart, M.A., A.E. Hubbard, M.E. van der Laan, J.M. Colford, and J.N.S. Eisenberg (2002). Statistical estimation of parameters in a disease transmission model. Statistics in Medicine, 21, 3627–3638.CrossRefPubMedGoogle Scholar
  18. [18]
    O’Neill, P.D. (2003). Perfect simulation for Reed-Frost epidemic models. Statistics and Computing, 13, 37–44.MathSciNetCrossRefGoogle Scholar
  19. [19]
    Britton, T. and P.D. O’Neill (2002). Statistical inference for stochastic epidemics in populations with random social structure. Scandinavian Journal of Statistics, 29, 375–390.CrossRefMathSciNetGoogle Scholar
  20. [20]
    Kurtz, T.G. (1970). Solutions of ordinary differential equations as limits of pure jump Markov processes. Journal of Applied Probability, 7, 49–58.zbMATHMathSciNetCrossRefGoogle Scholar
  21. [21]
    Kurtz, T.G. (1971). Limit theorems for sequences of jump Markov processes approximating ordinary differential processes. Journal of Applied Probability, 8, 344–356.zbMATHMathSciNetCrossRefGoogle Scholar
  22. [22]
    Clancy, D. and N.P. French (2001). A stochastic model for disease transmission in a managed herd, motivated by Neospora caninum amongst dairy cattle. Mathematical Biosciences, 170, 113–132.CrossRefPubMedMathSciNetGoogle Scholar
  23. [23]
    Pollett, P.K. (1990). On a model for interference between searching insect parasites. Journal of the Australian Mathematical Society, Series B, 31, 133–150.MathSciNetCrossRefGoogle Scholar
  24. [24]
    Nold, A. (1980). Heterogeneity in disease-transmission modeling. Mathematical Biosciences, 52, 227–240.CrossRefzbMATHMathSciNetGoogle Scholar
  25. [25]
    Soorapanth, S. (2002). Microbial Risk Models Designed to Inform Water Treatment Policy Decisions. PhD Thesis, University of Michigan, Ann Arbor, MI.Google Scholar
  26. [26]
    Osewe, P., D.G. Addiss, K.A. Blair, A. Hightower, M.L. Kamb, and J.P. Davis (1996). Cryptosporidiosis in Wisconsin: A case-control study of post-outbreak transmission. Epidemiology and Infection, 117, 297–304.PubMedCrossRefGoogle Scholar
  27. [27]
    Altmann, M. (1998). The deterministic limit of infectious disease models with dynamic partners. Mathematical Biosciences, 150, 153–175.CrossRefzbMATHPubMedGoogle Scholar
  28. [28]
    Nåsell, I. (1996). The quasi-stationary distribution of the closed endemic SIS Model. Advances in Applied Probability, 28, 895–932.zbMATHMathSciNetCrossRefGoogle Scholar
  29. [29]
    Chick, S.E. (2002). Approximations of stochastic epidemic models for parameter inference. Working Paper, INSEAD, Fontainbleau, France.Google Scholar
  30. [30]
    Koopman, J.S., S.E. Chick, C.S. Riolo, C.P. Simon, and J.A. Jacquez (2002). Stochastic effects on endemic infection levels of disseminating versus local contacts. Mathematical Biosciences, 180, 49–71.CrossRefPubMedMathSciNetGoogle Scholar
  31. [31]
    McNab, B.W. (1998). A general framework illustrating an approach to quantitative microbial food safety risk assessment. Journal of Food Protection, 61, 1216–1228.PubMedGoogle Scholar
  32. [32]
    Ferguson, N.M., C.A. Donnelly, and R.M. Anderson (2001). The foot-and-mouth epidemic in Great Britain: Pattern of spread and impact of interventions. Science, 292, 1155–1160.CrossRefADSPubMedGoogle Scholar
  33. [33]
    Simon, C.P. and J.A. Jacquez (1992). Reproduction numbers and the stability of equilibria of SI models for heterogeneous populations. SIAM Journal of Applied Mathematics, 52, 541–576.CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  • Stephen E. Chick
    • 1
  • Sada Soorapanth
    • 2
  • James S. Koopman
    • 3
    • 4
  1. 1.Technology Management Area FontainebleauINSEADFrance
  2. 2.Department of Industrial and Operations EngineeringUniversity of MichiganAnn Arbor
  3. 3.Department of EpidemiologyUniversity of MichiganAnn Arbor
  4. 4.Center for the Study of Complex SystemsUniversity of MichiganAnn Arbor

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