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Optimal Control Strategies on a TB-HIV/AIDS Coinfection

S. N. Rayhan, T. Bakhtiar, Jaharuddin

Abstract



In 2009, Bhunu et al. develop a tuberculosis (TB) and HIV/AIDS co-infection model which considers antiretroviral therapy for the AIDS cases and treatments for both latent and active forms of TB. The equilibrium quantities for the model are then determined by using stability analysis. In this work, the model was modified by transferring the treatment rates from static to dynamic form and determined by using optimal control theory, with the application of five different scenarios related to the control applications. Pontryagin maximum principle was applied to derive the differential equations system as a condition that must be satisfied by the optimal control variables. Furthermore, the fourth-order Runge-Kutta method was exploited to determine the numerical solution of the optimal control problem. In this numerical solution, it is shown that the controls treated on TB-HIV/AIDS co-infection model provide a good effect as both co-infected populations are decreasing.

Keywords


Pontryagin maximum principle, fourth-order Runge-Kutta method, tuberculosis, antiretroviral therapy

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