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The saturating contact rate in marriage- and epidemic models. (English) Zbl 0770.92021
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.

MSC:
92D30 Epidemiology
34D15 Singular perturbations of ordinary differential equations
34E15 Singular perturbations, general theory for ordinary differential equations
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