Transmission of infection along a dynamic sexual network with star-shaped components
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Currently there is a debate in epidemiology about the contribution of overlapping sexual partnerships, and in particular polygamy, to the spread of HIV in sub-Saharan Africa. Motivated by this debate we formulate a mathematical model for the dynamic sexual network corresponding to polygamy. Consider the following situation. Suppose we have a heterosexual population where men may have multiple wives and women at most one husband. If we also assume men and women to be faithful to each other, then this gives rise to a sexual network with multiple star-shaped components. This network is dynamic as partnerships are formed and broken over time and individuals enter and leave the population due to demographic turnover. We can describe this network with a system of ordinary differential equations (ODEs). We analyse the system and study existence and uniqueness of solutions and the steady state of the system. We are interested in how sexually transmitted infections, such as HIV, spread along the network. Therefore, the next part of the research is to superimpose an S(usceptible)-I(nfectious) infection on the dynamic sexual network and describe the infection model with a set of ODEs. Using the interpretation of the model we determine epidemic thresholds for the system. The thresholds allow us to determine what the conditions are for an infection to become endemic in the population. We end the analysis by comparing the basic reproduction numbers of the infectious disease models for the polygynous population with that of a monogamous population.