Statistics and Computing

, Volume 13, Issue 1, pp 37–44 | Cite as

Perfect simulation for Reed-Frost epidemic models

  • Philip D. O'Neill


The Reed-Frost epidemic model is a simple stochastic process with parameter q that describes the spread of an infectious disease among a closed population. Given data on the final outcome of an epidemic, it is possible to perform Bayesian inference for q using a simple Gibbs sampler algorithm. In this paper it is illustrated that by choosing latent variables appropriately, certain monotonicity properties hold which facilitate the use of a perfect simulation algorithm. The methods are applied to real data.

epidemics stochastic epidemic models Reed-Frost epidemic model perfect simulation Markov chain Monte Carlo methods Bayesian inference 


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  1. Addy C.L., Longini I.M., and Haber M. 1991. A generalized stochastic model for the analysis of infectious disease final size data. Biometrics 47: 961–974.Google Scholar
  2. Bailey N.T.J. 1975. The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. Griffin, London.Google Scholar
  3. Ball F.G. and O'Neill P.D. 1999. The distribution of general final state random variables for stochastic epidemic models. J. Appl. Prob. 36: 473–491.Google Scholar
  4. Becker N.G. 1989. Analysis of Infectious Disease Data. Chapman and Hall, London.Google Scholar
  5. Becker N.G. and Britton T. 1999. Statistical studies of infectious disease incidence. J. Roy. Stat. Soc. B 61: 287–307.Google Scholar
  6. Brooks S.P. and Roberts G.O. 1998. Assessing convergence of Markov Chain Monte Carlo algorithms. Statistics and Computing 8: 319–335.Google Scholar
  7. Casella G., Lavine M., and Robert C. 2000. Explaining the perfect sampler. Preprint.Google Scholar
  8. Gibson G.J. 1998. Markov chain Monte Carlo methods for fitting spatiotemporal stochastic models in plant epidemiology. Appl. Stat. 46: 215–233.Google Scholar
  9. Gilks W.R., Richardson S., and Spiegelhalter D.J. 1996. Markov Chain Monte Carlo in practice. Chapman and Hall, London.Google Scholar
  10. Heasman M.A. and Reid D.D. 1961. Theory and observation in family epidemics of the common cold. Brit. J. Prev. Soc. Med. 15: 12–16.Google Scholar
  11. Lefèvre C. and Picard P. 1990. A non-standard family of polynomials and the final size distribution of Reed-Frost epidemic processes. Adv. Appl. Prob. 22: 25–48.Google Scholar
  12. Longini I.M. and Koopman J.S. 1982. Household and community transmission parameters from final distributions of infections in households. Biometrics 38: 115–126.Google Scholar
  13. O'Neill P.D., Balding D.J., Becker N.G., Eerola M., and Mollison D. 2000. Analyses of infectious disease data from household outbreaks by Markov Chain Monte Carlo methods. Appl. Stat. 49: 517–542.Google Scholar
  14. O'Neill P.D. and Becker N.G. 2001. Inference for an epidemic when susceptibility varies. Biostatistics 2: 99–108.Google Scholar
  15. O'Neill P.D. and Roberts G.O. 1999. Bayesian inference for partially observed stochastic epidemics. J. Roy. Stat. Soc. A 162: 121–129.Google Scholar
  16. Propp J. and Wilson D. 1996. Exact sampling with coupled Markov chains and applications to statistical mechanics. Rand. Struct. Alg. 9: 223–252.Google Scholar
  17. Stoyan D. 1983. Comparison Methods for Queues and other Stochastic Models. Wiley, New York.Google Scholar

Copyright information

© Kluwer Academic Publishers 2003

Authors and Affiliations

  • Philip D. O'Neill
    • 1
  1. 1.School of Mathematical SciencesUniversity of NottinghamNottinghamEngland

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