Abstract
A deterministic mathematical model with educational campaigns and ARV (Anti Retro Viral) therapy as control variables are formulated and analyzed using optimal control theory (the Pontryagin’s Maximum Principle). We formulate the appropriate optimal control problem and investigate the necessary conditions for the disease control in order to determine the role of the asymptomatic stage and pre-AIDS stage of HIV infection and in the spread of HIV using of educational campaigns and antiretroviral therapy are used as the control items. The numerical simulation of both the systems i.e. with control and without control, shows that the combination of the two strategies helps to reduce a significant difference in the number of individuals in the asymptomatic stage of HIV infection, the number of individuals in pre-AIDS stage, and the number of individuals with full-blown AIDS.
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