Mathematical Modeling and Optimal Control of an HIV/AIDS Transmission Model

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In this article, we present a mathematical model for the transmission of HIV with the compartment of individuals in remission and vertical transmission describing the dynamics of the spread of the HIV/AIDS epidemic in a community. In the mathematical analysis of the model, we compute the basic reproduction number R0 and study the existence and stability of the disease-free equilibrium point. We also formulate an appropriate optimal control problem and study the conditions necessary for disease control to determine the role of preventive measures and treatment in reducing the spread of HIV/AIDS. Indeed, we study the impact of these control variables taken separately and combined. So we find that treatment is more cost-effective in reducing the spread of HIV than preventive measures. Finally, the numerical results conform to the theoretical analysis.

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