Computation of final outcome probabilities for the generalised stochastic epidemic
- 162 Downloads
This paper is concerned with methods for the numerical calculation of the final outcome distribution for a well-known stochastic epidemic model in a closed population. The model is of the SIR (Susceptible→Infected→ Removed) type, and the infectious period can have any specified distribution. The final outcome distribution is specified by the solution of a triangular system of linear equations, but the form of the distribution leads to inherent numerical problems in the solution. Here we employ multiple precision arithmetic to surmount these problems. As applications of our methodology, we assess the accuracy of two approximations that are frequently used in practice, namely an approximation for the probability of an epidemic occurring, and a Gaussian approximation to the final number infected in the event of an outbreak. We also present an example of Bayesian inference for the epidemic threshold parameter.
KeywordsStochastic epidemic models Markov chain Monte Carlo Methods Limit theorems Multiple precision arithmetic Final size
Unable to display preview. Download preview PDF.
- 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
- Andersson H. and Britton T. 2000. Stochastic Epidemic Models and Their Statistical Analysis, Springer Lecture Notes in Statistics, New York.Google Scholar
- Bailey N. T. J. 1975. The Mathematical Theory of Infectious Diseases and its Applications, 2nd edn. London: Griffin.Google Scholar
- Becker N. G. 1989. Analysis of Infectious Disease Data, Chapman and Hall, London.Google Scholar
- Dietz K. 1993. The estimation of the basic reproduction number for infectious diseases. Statistical methods in medical research 2: 23–41.Google Scholar
- Gilks W. R., Richardson S. and Spiegelhalter D. J. 1996. Markov Chain Monte Carlo in Practice. London: Chapman and Hall.Google Scholar