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Sexual partnerships that overlap in time (concurrent relationships) may playa significant role in the HIV epidemic, but the precise effect is unclear. Wederive edge-based compartmental models of disease spread in idealized dynamicpopulations with and without concurrency to allow for an investigation of itseffects. Our models assume that partnerships change in time and individualsenter and leave the at-risk population. Infected individuals transmit at aconstant per-partnership rate to their susceptible partners. In our idealizedpopulations we find regions of parameter space where the existence ofconcurrent partnerships leads to substantially faster growth and higherequilibrium levels, but also regions in which the existence of concurrentpartnerships has very little impact on the growth or the equilibrium.Additionally we find mixed regimes in which concurrency significantly increasesthe early growth, but has little effect on the ultimate equilibrium level.Guided by model predictions, we discuss general conditions under whichconcurrent relationships would be expected to have large or small effects inreal-world settings. Our observation that the impact of concurrency saturatessuggests that concurrency-reducing interventions may be most effective inpopulations with low to moderate concurrency.

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