LYAPUNOV STABILITY OF MALE CIRCUMCISION MODEL IN HIV/AIDS PREVENTIONS

This work examines the contribution of a non-pharmaceutical control measure, male circumcision to combat the spread of the world’s threatening infection, the HIV/AIDS. It establishes the condition for positivity and boundedness of the model, which enhance the existence and uniqueness of the solution of the model thereby making the model to be epidemiologically meaningful.The main mathematical technique used is the Lyapunov direct method which is applied successfully to two cases: when the population is not circumcised and when the population is fully circumcised, to study the global asymptotic stability of the model. It was established that the local stability of the model is guaranteed if the product of the probability of transmission by individuals and the average number of contact per unit time is less than the sum product of circumcision rate and that of the natural death of the individual in the population. That is if circumcision is encouraged in the population it greatly enhances the eradication of HIV/AIDS. When the population is circumcised the analysis showed that, the disease free equilibrium is globally asymptotically stable in Ω if Rc0 ≤ 1.