Mathematical Overview of Biochemical and Physical Interactions Considering Reverse Transcriptase and Integrase Enzymes to Explore HIV Progression: A Control Theoretic Approach

Successful replication of Human Immunodeficiency Virus requires viral genome reverse transcription to generate proviral DNA and integration into the target cell genome. In this research article, we explore the relative effect of physical interactions between two enzymes RT and IN on two of the most fundamental sequential processes in HIV replication, namely, reverse transcription and integration. Activities of these two pivotal enzymes are targets of antiretroviral drugs. We also investigate the crucial impact of these antiretroviral drugs on the control-induced mathematical model by incorporating two bounded control parameters into our system. More specifically, we apply the well-known Pontryagin minimum principle to minimize the concentrations of viral DNA and the pre-integration complex (PIC), utilizing two control functions: $$m_1(t)$$ as a reverse transcriptase inhibitor and $$m_2(t)$$ as an integrase inhibitor. We found that the affinity of RT and IN enzymes towards each other and the impacts of their direct interaction on the biochemical processes play pivotal roles in HIV replication dynamics, which further guide the development of a realistic optimal control-induced policy. All of our achieved analytical outcomes have been confirmed through numerical simulations.