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Biostatistics Advance Access published online on September 6, 2006
Biostatistics, doi:10.1093/biostatistics/kxl023
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© The Author 2006. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oxfordjournals.org
Received February 1, 2006
Revised August 30, 2006
Accepted August 30, 2006

Article

Non-homogeneous birth and death models for epidemic outbreak data

Jan van den Broek 1 * and Hans J.A.P. Heesterbeek 1

1 Faculty of Veterinary Medicine, Utrecht University, The Netherlands

* To whom correspondence should be addressed.
Jan van den Broek, E-mail: j.vandenbroek{at}vet.uu.nl


  Abstract

In this paper generalized non-linear models are proposed in order to incorporate the following considerations in modelling an epidemic disease outbreak statistically. 1) The dependence of the data is handled with a non-homogeneous death or a non-homogeneous birth process. 2) The first stage of the outbreak is described with an epidemic Susceptibles-Infectives-Removed (SIR) model. Soon the control measures taken will dominate the process. These measures are in addition to the natural epidemic removal process. The prevalence is related to the censored infection times in such a way that the distribution function and thus the survival function satisfy approximately the first equation of the SIR model. This leads in a natural way to the Burr family of distributions. 3) The non-homogeneous birth process handles the fact that in practice, with some delay, infected are registered, but not susceptibles. 4) Finally the ending of the epidemic caused by the measures taken is incorporated through a modification of the survival function with a final size parameter, in the same way as is done in long-term survival models. These models are applied to three outbreaks: The Dutch classical swine fever outbreak from 1997-1998, the foot and mouth disease outbreak in Great Britain from 2001 and the Dutch avian influenza (H7N7) outbreak from 2003.

Keywords: Non-homogeneous birth process; Reproductive power; Force of infection; Non-homogeneous death process; Burr distribution; Classical swine fever; Avian influenza (H7N7); Foot and mouth disease; Negative binomial.
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