THE SATURATING CONTACT RATE IN MARRIAGE AND EPIDEMIC MODELS

In this note we show how to derive, by a mechanistic argument, an expr ession for the saturating contact rate of individual contacts in a pop ulation that mixes randomly. The main assumption is that the individua l 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 individu al. In special cases an explicit formula for the contact rate is obtai ned. The result is applied to mathematical epidemiology and marriage m odels.