Saturation Effects and the Concurrency Hypothesis: Insights from an Analytic Model

TL;DR

This paper develops an analytic model to understand how concurrent sexual partnerships influence HIV spread, revealing that their impact varies across different population parameters and may saturate, affecting intervention strategies.

Contribution

It introduces a novel edge-based compartmental model to analyze the effects of concurrency on disease dynamics in dynamic populations.

Findings

Concurrency can lead to faster epidemic growth and higher equilibrium levels in certain conditions.

The impact of concurrency saturates, suggesting limited benefits of reducing concurrency in high levels.

Early epidemic growth is significantly affected by concurrency, but long-term levels may not be.

Abstract

Sexual partnerships that overlap in time (concurrent relationships) may play a significant role in the HIV epidemic, but the precise effect is unclear. We derive edge-based compartmental models of disease spread in idealized dynamic populations with and without concurrency to allow for an investigation of its effects. Our models assume that partnerships change in time and individuals enter and leave the at-risk population. Infected individuals transmit at a constant per-partnership rate to their susceptible partners. In our idealized populations we find regions of parameter space where the existence of concurrent partnerships leads to substantially faster growth and higher equilibrium levels, but also regions in which the existence of concurrent partnerships has very little impact on the growth or the equilibrium. Additionally we find mixed regimes in which concurrency significantly increases the early growth, but has little effect on the ultimate equilibrium level. Guided by model predictions, we discuss general conditions under which concurrent relationships would be expected to have large or small effects in real-world settings. Our observation that the impact of concurrency saturates suggests that concurrency-reducing interventions may be most effective in populations with low to moderate concurrency.