The informal settlement of Kibera in Nairobi has a significantly higher prevalence of HIV than the Kenyan average. Sex workers and their male clients from Kibera were recently surveyed; their responses indicate a population that is well mixed with large variance in individual number of sexual contacts. Hence, a multigroup two-sex model is created to study HIV spread in the sex working population of Kibera. This model is parameterized to the Kibera data, and the e ffects of various parameters on the prevalence of HIV and the risk of infection to individuals are studied by an elasticity analysis. The probability of infection from males to females per sexual act has the greatest implications for HIV control. A simplified model is presented and a theoretical analysis gives the reproduction number and proves global stability of the endemic equilibrium. / Graduate