Modeling a Sexual Network Using Graph Theory and the Simulation of Prevalence and Spread of Human Immunodeficiency Virus (hiv) in the Network

The application of mathematical methods in epidemiology cannot be over emphasized. An area which has seen a remarkable development recently is the modeling, simulation and analysis of contagion networks. On the other hand, HIV/AIDS have remained endemic especially in sub-Saharan Africa spreading primarily through sex. This calls for a critical study of the contagion network of the most sexually active portion of the population to understand the structure and behavior of this network. This research modeled the sexual networks of some selected sex workers and their clients using the mathematical graph theory. Furthermore, using statistics obtained from two HIV clinics and the National Action Committee on Aids, the research simulated the prevalence and spread of HIV/AIDS in the modeled networks. Results indicate that in agreement with the widely held notion of scale-free, the networks have long-tailed power-law degree distribution with an exponent 𝛾 = 2.9 (0.3) for females, and 𝛾 =2.7 (0.2) for males and tend to be concentrated around sex workers with younger age who do not live in brothels. Furthermore, the observed networks exhibit a low variance in the number of contacts most sex-workers have over the given time period the study was carried out.