# Optimal Control Strategy to Reduce the Infection of Pandemic HIV Associated with Tuberculosis

## DOI:

https://doi.org/10.5614/cbms.2022.5.1.2## Keywords:

Mathematical model, HIV and TB co-infection, Optimal control, Pontryagin's Maximum Principle## Abstract

Tuberculosis (TB) and HIV/AIDS has become hazardous among communicable diseases and so as their co-infection in present era. HIV virus gradually weakens immune system in human body, and then TB infects with the assist of HIV/AIDS at any stage of the total infectious period. Today, HIV and tuberculosis (TB) are the main causes of mortality from infectious and chronic diseases. In this Study, we manifest a compartmental co-infection model including HIV and TB on the basis of their characteristics of disease transmission. The model is divided into 10 compartments, each with its own set of nonlinear ordinary differential equations. Using the Pontryagin's Maximum Principle, we investigate the existence of state variables, objective functional and optimum control plans. Identifying the most effective ways for reducing infection among the individuals, the optimal control techniques like vaccination control and treatment control measures are applied. The goal of this study is to lower the rate of HIV-TB co-infection and the cost of treatment. Another objective is to find the better control strategy to prevent HIV/AIDS that invites other pathogen in human body by gradual loosing of immunity. We carried out the investigation both analytically and numerically to divulge the effectiveness of the vaccination and treatment control to lessen the HIV and TB infection among the individuals.

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