Journal of Mathematical Biology

, Volume 31, Issue 5, pp 529–539

The saturating contact rate in marriage- and epidemic models

  • J. A. P. Heesterbeek
  • J. A. J. Metz

DOI: 10.1007/BF00173891

Cite this article as:
Heesterbeek, J.A.P. & Metz, J.A.J. J. Math. Biol. (1993) 31: 529. doi:10.1007/BF00173891


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.

Key words

Contact rate Time-scale arguments Mass-action kinetics Epidemic models Marriage models 

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • J. A. P. Heesterbeek
    • 1
  • J. A. J. Metz
    • 2
  1. 1.Centre for Mathematics and Computer Science (CWI)AmsterdamThe Netherlands
  2. 2.Institute of Theoretical BiologyUniversity of LeidenLeidenThe Netherlands