Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic - Jeff Musgrave; James Watmough (Mathematical Biosciences and Engineering)
Since the discovery of HIV/AIDS there have been numerous mathematical modelsproposed to explain the epidemic of the disease and to evaluate possiblecontrol measures. In particular, several recent studies have looked at thepotential impact of condom usage on the epidemic[1, 2, 3, 4]. We develop a simplemodel for HIV/AIDS, and investigate the effectiveness of condoms as apossible control strategy. We show that condoms can greatly reduce the numberof outbreaks and the size of the epidemic. However, the necessary condom usagelevels are much higher than the current estimates. We conclude that condomsalone will not be sufficient to halt the epidemic in most populationsunless current estimates of the transmission probabilities are high.Our model has only five independentparameters, which allows for a complete analysis. We show that the assumptionsof mass action and standard incidence provide similar results, which impliesthat the results of the simpler mass action model can be used as a good firstapproximation to the peak of the epidemic.