Interaction, Pair Formation and Force of Infection Terms in Sexually Transmitted Diseases

A central question in the study of the dynamics of sexually-transmitted diseases — one emphasized by the AIDS epidemic — is that of mixing. In this note we formulate a generalization of the Blythe and Castillo-Chavez social/sexual framework for human interactions through the incorporation of age-structure, and derive an explicit expression for the general solution to this formulation. An age-structured epidemic model for a single sexually-active homosexual population, stratified by risk and age, with arbitrary risk and age-dependent mixing and variable infectivity is formulated. In the special case of proportionate mixing in age and risk, an explicit expression for the basic reproductive number is given.