Saturating Contact Rate in Marriage- and Epidemic Models

摘要

How to derive, by a mechanistic argument, an expression for the saturatingcontact rate of individual contacts in a population that mixes randomly is shown. 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.