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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.

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