Biostatistics 3:493-510 (2002)
© 2002 Oxford University Press
A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks
Department of Statistics, University of Warwick, Coventry, CV4 7AL, UK and Department of Zoology, University of Cambridge, Cambridge, CB2 3EJ, UK stsbe{at}csv.warwick.ac.uk
Department of Entomology, Penn State University, PA 16802, USA
Department of Zoology, University of Cambridge, Cambridge, CB2 3EJ, UK
*To whom correspondence should be addressed
Epidemic dynamics pose a great challenge to stochastic modelling because chance events are major determinants of the size and the timing of the outbreak. Reintroduction of the disease through contact with infected individuals from other areas is an important latent stochastic variable. In this study we model these stochastic processes to explain extinction and recurrence of epidemics observed in measles. We develop estimating functions for such a model and apply the methodology to temporal case counts of measles in 60 cities in England and Wales. In order to estimate the unobserved spatial contact process we suggest a method based on stochastic simulation and marginal densities. The estimation results show that it is possible to consider a unified model for the UK cities where the parameters depend on the city size. Stochastic realizations from the dynamic model realistically capture the transitions from an endemic cyclic pattern in large populations to irregular epidemic outbreaks in small human host populations.
Keywords: Discrete latent variable; Population dynamics; Stochastic modelling of infectious diseases; Stochastic simulation; Time series of counts
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