The saturating contact rate in marriage- and epidemic models.
In this note 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.
Heesterbeek
J A
JA
Centre for Mathematics and Computer Science (CWI), Amsterdam, The Netherlands.
Metz
J A
JA
D000163:Acquired Immunodeficiency Syndrome / Q000453:epidemiology / Q000635:transmission; D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission; D005260:Female; D006801:Humans; D008297:Male; D008393:Marriage; D008433:Mathematics; D008962:Models, Theoretical; D013997:Time Factors