An Optimal Control Strategy for Antiretroviral Treatment of HIV Infection in Presence of Immunotherapy

Human immunodeficiency virus infection destroys immune system of an HIV infected individual, which results in the risk of other life threatening diseases such as kidney disease, liver disease, diabetes and some types of cancer. To date, there is no cure of this infectious disease, however, there exist antiretroviral drugs which help an HIV infected individual to live a quality life. But, these antiretroviral drugs are costly and have different side effects. Recent studies indicate that immunotherapy can be used in addition to these antiretroviral drugs for better management of HIV infection. In this study, we consider an HIV infection model incorporating the effects of antiretroviral drugs and immunotherapy. We verify that the model solutions are non-negative and bounded in the feasible domain. Stability analysis of HIV infection-free equilibrium point indicates that HIV is eradicated for a basic reproduction number less than one. In order to maximize healthy CD4 + T cells with minimum cost and side effects of drugs, we propose an optimal control problem with two different objectives. The optimal control problems are solved using discretization and large-scale optimization methods. We obtain optimal treatment strategies for antiretroviral drugs and immune boosting drugs.