The main purpose of this paper is to find the optimal control strategy for the elimination of HIV/AIDS in Nigeria. Using contemporary strategies in control of HIV in Nigeria such as counseling and condom use, we formulated the optimal control problem. The existence for the optimal control is established and the Pontryagin’s maximum principle is used to characterize these controls. The optimality system is derived and solved numerically using MATLAB. Our results showed that if all the proposed control measures are implemented with maximum effort HIV transmission will cease within ten years and the diseases will be completely eliminated from the country in the next 30 years.
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