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Examination of a simple model of condom usage and individual withdrawal for the HIV epidemic. (English) Zbl 1167.92029

Summary: Since the discovery of HIV/AIDS there have been numerous mathematical models proposed to explain the epidemic of the disease and to evaluate possible control measures. In particular, several recent studies have looked at the potential impact of condom usage on the epidemic. We develop a simple model for HIV/AIDS, and investigate the effectiveness of condoms as a possible control strategy. We show that condoms can greatly reduce the number of outbreaks and the size of the epidemic. However, the necessary condom usage levels are much higher than the current estimates. We conclude that condoms alone will not be sufficient to halt the epidemic in most populations unless current estimates of the transmission probabilities are high. Our model has only five independent parameters, which allows for a complete analysis. We show that the assumptions of mass action and standard incidence provide similar results, which implies that the results of the simpler mass action model can be used as a good first approximation to the peak of the epidemic.

MSC:

92D30 Epidemiology
93C95 Application models in control theory
37N25 Dynamical systems in biology
93C15 Control/observation systems governed by ordinary differential equations
92C60 Medical epidemiology
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