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The saturating contact rate in marriage- and epidemic models

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Abstract

In this note we show how to derive, by a mechanistic argument, an expression for the saturating contact rate of individual contacts in a population that mixes randomly. The main assumption is that the individual interaction times are typically short as compared to the time-scale of changes in, for example, individual-type, but that the interactions yet make up a considerable fraction of the time-budget of an individual. In special cases an explicit formula for the contact rate is obtained. The result is applied to mathematical epidemiology and marriage models.

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Authors and Affiliations

  1. Centre for Mathematics and Computer Science (CWI), P.O. Box 4079, NL-1009 AB, Amsterdam, The Netherlands

    J. A. P. Heesterbeek

  2. Institute of Theoretical Biology, University of Leiden, P.O. Box 9516, NL-2300 RA, Leiden, The Netherlands

    J. A. J. Metz

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  1. J. A. P. Heesterbeek
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  2. J. A. J. Metz
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Heesterbeek, J.A.P., Metz, J.A.J. The saturating contact rate in marriage- and epidemic models. J. Math. Biol. 31, 529–539 (1993). https://doi.org/10.1007/BF00173891

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  • DOI: https://doi.org/10.1007/BF00173891

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