Abstract
Malaria and HIV are two of the most serious global health challenges affecting developing countries. To have a deeper understanding of the two diseases, we developed a deterministic mathematical model with fourteen compartments on the transmission dynamics of HIV-Malaria Co-infections. The boundary of the model solution is performed, and we proceed to determine both the disease-free equilibrium (DFE) and the endemic equilibrium (EE) for the system of the equations. The next-generation matrix method is used to determine the basic reproductive number R 0 necessary for disease control. The basic model is extended into an optimal control problem by incorporating four control strategies, The Pontryagin’s maximum principle is employed to derive the necessary conditions for the existence of optimal control. Numerical results are displayed graphically. The results of the analysis show that the best approach to control the HIV-malaria co-infection is to combine both HIV control measures and malaria disease control measures on HIV-malaria co-infection patients. Keywords: HIV-Malaria Co-Infection, Pontryagin’s Maximum Principle, Hamiltonian DOI： https://doi.org/10.35741/issn.0258-2724.58.1.44
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