### Abstract

Does concurrency (the overlap in time of multiple partnerships) enhance the spread of HIV? Opinions differ! For a long time now, there is a debate about the role concurrency plays in the HIV epidemic in sub-Saharan Africa. In this region, HIV is widespread among heterosexual populations, which is very different from the rest of the world, where HIV remains concentrated in specific high risk groups such as injecting drug users. If concurrency is driving the HIV epidemic in sub-Saharan Africa, then prevention and intervention programs need to be designed to target this. However, we first need to understand how concurrency actually impacts the spread of HIV. In this project, a mathematical modelling approach is used.

A mathematical framework for a dynamic sexual network incorporating demography was constructed and two theoretical measures for concurrency were defined: the individual- and the partnership- based concurrency index. For this network, the concurrency indices were characterized. Next, an SI-infection was superimposed on the network. The epidemiological quantities $R_0$, the Malthusian parameter $r$, and the endemic level were characterized for the infection on the network.

In this project we investigate how these epidemiological quantities relate to the concurrency indices that are defined in the theoretical framework. We also consider several measures for concurrency used in empirical work and investigate if they have the same relation to the infectious disease dynamics. This project, that takes a mathematical modelling approach, can be used as an epidemiological tool that provides a general framework for investigating the concurrency hypothesis. This in turn can guide us in future prevention message but also in what parameters and quantities should be measured in the field.