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Analysing Outbreak Data in a Heterogeneous Population with Migration
Modeling and Control in Biomedical Systems, Volume # 7 | Part# 1
Authors
Wolkewitz, Martin; Schumacher, Martin
Identifier
10.3182/20090812-3-DK-2006.00054
Index Terms
Bioinformatics
Abstract
Mathematical modelling of infectious diseases gains growing attention in epidemiology during the last decades. The major benefits of simulating compartmental models are the prediction of the consequences of potential interventions, a deeper understanding of epidemicdynamics and clinical decision support. The main limitation is however that several parameters are based on uncertain expert guesses (default values) and are not estimated from the study data. In this paper we build a bridge between the well-known deterministic S-I-R (Susceptible-Infectious-Removed) model which can be described with differential equations and the stochastic counterpart which can be used for statistical inference if outbreak data on an individual patient level are available. The possibly time-dependent transmission rate as well as the (basic) reproduction number are the main epidemiological parameters of interest. Furthermore, one important type of heterogeneity is considered: individuals may vary due to their susceptibility, i.e., risk factors for infection may be investigated. The Cox-Aalen survival model that is based on a multiplicative-additive hazard structure turned out to be a suitable tool for that purpose. The results give valuable informations for clinicians working in infection control and public health.
References
REFERENCES Becker, N.G. (1989). Analysis of infectious disease data. Chapman and Hall Ltd, New York, first edition. Becker, N. and Britton, T. (1999). Statistical studies of infectious disease incidence. Journal of the Royal Statistical Society: Series B: Statistical Methodology, 61(2), 287-307. Brauer, F. (2008). Compartmental models in epi- demiology. LECTURE NOTES IN MATHEMATICSSPRINGER- VERLAG-, 1945, 19. Cooper, B., Medley, G., Bradley, S., and Scott, G. (2008). An augmented data method for the analysis of nosoco- mial infection data. Am. J. Epidemiol., 168, 548-557. R Development Core Team (2005). R: A language and environment for statistical computing. R Founda- tion for Statistical Computing, Vienna, Austria. URL http://www.R-project.org. ISBN 3-900051-07-0. Rhodes, P., Halloran,M., and Longini Jr, I. (1996). Count- ing process models for infectious disease data: distin- guishing exposure to infection from susceptibility. Journal of the Royal Statistical Society. Series B (Methodological) , 751-762. Scheike, T. and Zhang, M. (2003). Extensions and ap- plications of the Cox-Aalen survival model. Biom., 59, 1036-1045. Wolkewitz, M., Dettenkofer, M., Bertz, H., Schumacher, M., and Huebner, J. (2008a). Environmental contam- ination as an important route for the transmission of VRE: Modeling and prediction of classical interventions. Infectious Disease: Research and Treatment, 1, 3-11. Wolkewitz, M., Dettenkofer, M., Bertz, H., Schumacher, M., and Huebner, J. (2008b). Statistical epidemic modeling with hospital outbreak data. Stat Med, 27, 6522-6531. Yan, P. (2008). Distribution Theory, Stochastic Pro- cesses and Infectious Disease Modelling. LECTURE NOTES IN MATHEMATICS-SPRINGER-VERLAG-, 1945, 229.