Heesterbeek, J. A. P.; Metz, J. A. J. The saturating contact rate in marriage- and epidemic models. (English) Zbl 0770.92021 J. Math. Biol. 31, No. 5, 529-539 (1993). Summary: 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. Cited in 2 ReviewsCited in 58 Documents MSC: 92D30 Epidemiology 34D15 Singular perturbations of ordinary differential equations 34E15 Singular perturbations for ordinary differential equations Keywords:time-scale arguments; mass-action kinetics; random mixing; saturating contact rate of individual contacts; marriage models PDFBibTeX XMLCite \textit{J. A. P. Heesterbeek} and \textit{J. A. J. Metz}, J. Math. Biol. 31, No. 5, 529--539 (1993; Zbl 0770.92021) Full Text: DOI