Modeling disease spread in populations with birth, death, and concurrency

The existence of sexual partnerships that overlap in time (concurrent relationships) is believed by some to be a significant contributing factor to the spread of HIV, although this is controversial. We derive an analytic model which allows us to investigate and compare disease spread in populations with and without concurrency. We can identify regions of parameter space in which its impact is negligible, and other regions in which it plays a major role. We also see that the impact of concurrency on the initial growth phase can be much larger than its impact on the equilibrium size. We see that the effect of concurrency saturates, which leads to the perhaps surprising conclusion that interventions targeting concurrency may be most effective in populations with low to moderate levels of concurrency. Author Summary We consider the spread of an infectious disease through a population modeled by a dynamic network with demographic turnover. We develop a stochastic model of the disease and derive governing equations that exactly predict the large population (deterministic) limit of the stochastic model. We use this to investigate the role of concurrency and find that interventions targeting concurrency may be most effective in populations with lower levels of concurrency. Our model is not intended to be an accurate representation of any single population. Rather it is intended to give general insights for intervention design and to provide a framework which can be further specialized to particular populations. This model is the first model to allow for analytic investigation of the impact of concurrent partnerships in a population exhibiting demographic turnover. Thus it will be useful for investigating the “concurrency hypothesis.”