Optimal control of HIV resistance and tuberculosis co-infection using treatment intervention

In this paper we presented a mathematical model of the spread of HIV and tuberculosis (TB) co-infection considering the resistance of HIV to antiretroviral (ARV) drugs. The model also included anti-TB and ARV treatments as system control variables. For the model without controls, we investigated the existence and stability of equilibria based on three basic reproduction numbers corresponding to the TB and two strains HIV infection. We also performed sensitivity analysis to determine the dominant factor controlling the spread. Then, the optimal control condition was derived using Pontryagin Maximum Principle on the model to achieve the goal of minimizing the number of infected population. The numerical simulations of the optimal control were also performed to illustrate the results.