Pair formation models for sexually transmitted infections: A primer

Abstract

For modelling sexually transmitted infections, duration of partnerships can strongly influence the transmission dynamics of the infection. If partnerships are monogamous, pairs of susceptible individuals are protected from becoming infected, while pairs of infected individuals delay onward transmission of the infection as long as they persist. In addition, for curable infections re-infection from an infected partner may occur. Furthermore, interventions based on contact tracing rely on the possibility of identifying and treating partners of infected individuals. To reflect these features in a mathematical model, pair formation models were introduced to mathematical epidemiology in the 1980's. They have since been developed into a widely used tool in modelling sexually transmitted infections and the impact of interventions. Here we give a basic introduction to the concepts of pair formation models for a susceptible-infected-susceptible (SIS) epidemic. We review some results and applications of pair formation models mainly in the context of chlamydia infection.

Keywords: Basic reproduction number; Mathematical model; Pair formation; Partnership duration; Sexually transmitted infections.

Fig. 1

Flow scheme for the SIS pair formation model.

Fig. 2

Illustration of infections that can go back and forth between persons. In this example the initial case (top row) transmitted the infection twice to the partner (a and b). The case reproduction number in this example would be 1 (since the initial case only infected one person), but the basic reproduction number would be 2 (since the partner became infected twice). Black arrows denote initial infection and grey dashed arrows re-infections.

Fig. 3

A typical distribution of numbers of partners in the last year reported in a heterosexual population. Most respondents report 0–1 partners, a small fraction report more than five partners. Based on data from Johnson et al. (2001).

Fig. 4

This figure illustrates different intervention measures for controlling chlamydia transmission. First, asymptomatically infected individuals are actively found and treated through screening (either when they are single or in a pair). When tested positive for chlamydia, partner notification can be initiated and positive partners can also be treated. When partner notification is unsuccessful, the index case can become re-infected from her infected partner. For illustration purposes, we assumed that treatment is 100% effective.