Frequency–dependent incidence in models of sexually transmitted diseases: portrayal of pair–based transmission and effects of illness on contact behaviour

James O. Lloyd-Smith, Wayne M. Getz, Hans V. Westerhoff

Abstract

We explore the transmission process for sexually transmitted diseases (STDs). We derive the classical frequency–dependent incidence mechanistically from a pair–formation model, using an approximation that applies to populations with rapid pairing dynamics (such as core groups or non–pair–bonding animals). This mechanistic derivation provides a framework to assess how accurately frequency–dependent incidence portrays the pair–based transmission known to underlie STD dynamics. This accuracy depends strongly on the disease being studied: frequency–dependent formulations are more suitable for chronic less–transmissible infections than for transient highly transmissible infections. Our results thus support earlier proposals to divide STDs into these two functional classes, and we suggest guidelines to help assess under what conditions each class can be appropriately modelled using frequency–dependent incidence. We then extend the derivation to include situations where infected individuals exhibit altered pairing behaviour. For four cases of increasing behavioural complexity, analytic expressions are presented for the generalized frequency–dependent incidence rate, basic reproductive number (R0) and steady–state prevalence (i) of an epidemic. The expression for R0 is identical for all cases, giving refined insights into determinants of invasibility of STDs. Potentially significant effects of infection–induced changes in contact behaviour are illustrated by simulating epidemics of bacterial and viral STDs. We discuss the application of our results to STDs (in humans and animals) and other infectious diseases.