Center of Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, West Bengal, Kolkata, India

Abstract. Despite significant advancements in antiretroviral therapy, the complete eradication of HIV remains a major challenge due to the intricate intracellular kinetics of viral replication. HIV replication depends on two critical biochemical processes, reverse transcription and integration facilitated by the enzymes reverse transcriptase and integrase within activated T cells. In this study, we develop a mathematical model to characterize the intracellular dynamics of HIV replication, explicitly incorporating the interactions mediated by reverse transcriptase and integrase. The model is calibrated using experimental data through least squares fitting, ensuring precise parameter estimation and validation. We employ impulsive differential equations to explore the pharmacological action of Cabenuva, allowing us to investigate the dynamic intracellular response to treatment. Post-fitting correlation matrices and heat maps identify key parameters governing HIV replication and treatment efficacy, enabling the optimization of an impulsive dosing regimen for high-transmission-probability scenarios of the viral genome into the T cell cytoplasm. Our comprehensive analytical and numerical analysis suggests that an impulsive regimen of Cabenuva, with a fixed dosage of 0.2 μg/mm³ administered at 30-day intervals, can achieve viral eradication within one year. This regimen, validated through extensive Monte Carlo simulations, demonstrates superior control of free virion production. These findings provide different insights into the intracellular replication of HIV and propose a refined therapeutic strategy that could enhance current treatment protocols.

Key words: HIV, biochemical interaction, intracellular kinetics, viral RNA, viral DNA, impulsive therapy, Cabenuva