Advertisement

Parameter Estimation and Site-Specific Calibration of Disease Transmission Models

  • Robert C. Spear
  • A. Hubbard
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 673)

Abstract

The use of mathematical models for developing management options for controlling infectious diseases at a local scale requires that the structure and parameters of the model reflect the realities of transmission at that scale. Data available to inform local models are generally sparse and come from diverse sources and in diverse formats. These characteristics of the data and the complex structure of transmission models, result in many different parameter sets which mimic the local behavior of the system to within the resolution of field data, even for a model of fixed structure. A Bayesian approach is described, at both a practical and a theoretical level, which involves the assignment of prior parameter distributions and the definition of a semi-quantitative goodness of fit criteria which are essentially priors on the observable outputs. Monte Carlo simulations are used to generate samples from the posterior parameter space. This space is generally much more constrained than the prior space, but with a highly complex multivariate structure induced by the mathematical model. In applying the approach to a model of schistosomiasis transmission in a village in southwestern China, calibration of the model was found to be sensitive to the effective reproductive number, R eff . This finding has implications both for computation time for the Monte Carlo analysis and for the specification of field data to efficiently calibrate the model for transmission control.

Keywords

Posterior Distribution Pass Rate Reproductive Number Schistosoma Japonicum Schistosomiasis Japonicum 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Anderson RM, May RM. Infectious diseases of humans: Dynamics and control: Oxford Science Publications, 1991.Google Scholar
  2. 2.
    Spear R, Hornberger G. Eutrophication in Peel Inlet: II. Identification of critical uncertainties via generalized sensitivity analysis. Water Research 1980; 14:43–49.CrossRefGoogle Scholar
  3. 3.
    Beck M, Ravetz J, Mulkey L et al. On the problem of model validation for predictive exposure assessments. Stochas Hydrol Hydraulics 1997; 11:229–254.CrossRefGoogle Scholar
  4. 4.
    Spear RC. Large simulation models: Calibration, uniqueness and goodness of fit. Environmental Modeling and Software 1998; 12:219–228.CrossRefGoogle Scholar
  5. 5.
    Box G, Jenkins G, Reinsel G. Time Series Analysis: Forecasting And Control. 4th ed: John Wiley, 2008.Google Scholar
  6. 6.
    Chatfield C. The Analysis Of Time Series: An Introduction. 6th ed: CRC Press, 2004.Google Scholar
  7. 7.
    Beven K, Freer J. Equafinality, data assimilation and uncertainty estimation in mechanistic modeling of complex environmental systems using the GLUE methodology. J Hydrology 2001; 249:11–29.CrossRefGoogle Scholar
  8. 8.
    Poole D, Raftery AE. Inference for deterministic simulation models: The Bayesian melding approach. J Am Stat Assn 2000; 95:1244–1255.CrossRefGoogle Scholar
  9. 9.
    Grieb TM, Shang N, Spear RC et al. Examination of model uncertainty and parameter interaction in the global carbon cycling model. Environ Intl 1999; 25:787–803.CrossRefGoogle Scholar
  10. 10.
    Beven K. Prophecy, reality and uncertainty in distributed hydrological modeling. Adv Water Resources 1993; 16:41–51.CrossRefGoogle Scholar
  11. 11.
    Liang S, Maszle DM, Spear RC. A quantitative framework for a multi-group model of schistosomiasis japonicum transmission dynamics and control in Sichuan, China. Acta Tropica 2002; 82:263–277.PubMedGoogle Scholar
  12. 12.
    Macdonald G. The dynamics of helminth infections, with special reference to schistosomes. Trans R Soc Trop Med Hyg 1965; 59(5):489–506.CrossRefPubMedGoogle Scholar
  13. 13.
    Spear R, Seto E, Liang S et al. Factors influencing the transmission of schistosoma japonicum in the mountains of Sichuan province. Am J Trop Med Hyg 2004; 70(10):48–56.PubMedGoogle Scholar
  14. 14.
    Liang S, Spear RC, Seto E et al. A multi-group model of schistosoma japonicum transmission dynamics and control: model calibration and control prediction. Trop Med Intl Health 2005; 10:263–278.CrossRefGoogle Scholar
  15. 15.
    Liang S, Seto E, Remais J et al. Environmental effects on parasitic disease transmission exemplified by schistosomiasis in western China. PNAS 2007; 104:7110–7115.CrossRefPubMedGoogle Scholar
  16. 16.
    Woolhouse MEJ. On the application of mathematical models of schistosome transmission dynamics. II. Control. Acta Tropica 1992; 50:189–204.CrossRefPubMedGoogle Scholar
  17. 17.
    Spear RC, Hubbard A, Liang S et al. The use of disease transmission models for public health decision-making: Towards an approach for designing intervention strategies for schistosomiasis japonicum. Environ Hlth Perspectives 2002; 110:907–915.CrossRefGoogle Scholar

Copyright information

© Landes Bioscience and Springer Science+Business Media 2010

Authors and Affiliations

  • Robert C. Spear
    • 1
  • A. Hubbard
    • 1
  1. 1.Center for Occupational and Environmental Health, School of Public HealthUniversity of CaliforniaBerkeley

Personalised recommendations