Algorithms for efficiently and effectively matching agents in microsimulations of sexually transmitted infections

Mathematical models of the HIV epidemic have been used to estimate incidence, prevalence and life-expectancy, as well the benets and costs of public health interventions, such as the provision of antiretroviral treatment. Models of sexually transmitted infection epidemics attempt to account for varying levels of risk across a population based on diverse | or heterogeneous | sexual behaviour. Microsimulations are a type of model that can account for fine-grained heterogeneous sexual behaviour. This requires pairing individuals, or agents, into sexual partnerships whose distribution matches that of the population being studied, to the extent this is known. But pair-matching is computationally expensive. There is a need for computer algorithms that pair-match quickly. In this work we describe the role of modelling in responses to the South African HIV epidemic. We also chronicle a three-decade debate, greatly influenced since 2008 by a mathematical model, on the optimal time for people with HIV to start antiretroviral treatment. We then present and analyse several pair-matching algorithms, and compare them in a microsimulation of a fictitious STI. We find that there are algorithms, such as Cluster Shuffle Pair-Matching, that offer a good compromise between speed and approximating the distribution of sexual relationships of the study-population. An interesting further finding is that infection incidence decreases as population increases, all other things being equal. Whether this is an artefact of our methodology or a natural world phenomenon is unclear and a topic for further research