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Mathematical modelling of HIV-1 transcription inhibition: a comparative study between optimal control and impulsive approach

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Through the utilization of a proactive approach, interaction with human immunodeficiency virus type I (HIV-1) is facilitated, enabling the sequential stages of its fusion mechanism to be navigated successfully. As a result, the efficient infiltration of a target \(CD4^+T\) helper cell within the host organism by the virus is achieved. The onset of the virus’s replication cycle is initiated through this infiltration. As a retrovirus, the orchestration of the conversion of its single-stranded viral RNA genome into a more stable double-stranded DNA structure by HIV-1 is observed. Integration of this newly formed DNA with the host cell’s genetic material occurs. This pivotal transformation of the integrated pro-viral DNA into fully functional messenger RNA (mRNA) is facilitated by the host enzyme RNA polymerase II (Pol II). The central focus of the present ongoing research involves the construction of a meticulous mathematical framework consisting of a system of nonlinear differential equations. The investigation of the impact of a Tat inhibitor on the suppression of the transcriptional activity of HIV-1 is the aim of this inquiry. The perspective of an optimal control problem is assumed for this investigation. Furthermore, the assessment of the efficacy of the Tat inhibitor as a potential therapeutic intervention for HIV-1 infection is undertaken. Integration of a one-dimensional impulsive differential equation model, which determines a mathematically derived maximum concentration of the elongating complex (\(P_2\)), is employed for this assessment. The crucial aspect of this investigation is the consideration of the optimal timing between successive dosages. A comparative analysis is conducted to evaluate the distinct effects of continuous dosing versus impulse dosing of the Tat inhibitor. Numerical analysis is employed to contrast the outcomes of these dosing strategies. The present findings highlight that impulsive dosing demonstrates superior effectiveness compared to continuous dosing in the inhibition of HIV-1 transcription. Ultimately, the model’s parameter sensitivities are visualized through graphical representations. These visualizations serve to enhance the understanding of the underlying physiological and biochemical processes within this intricate system.

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The authors are grateful to the unanimous reviewers for their fruitful comments and suggestions. Srijita Mondal was the recipient of the “Innovation in Science Pursuit for Inspired Research” (INSPIRE) Program Fellowship (Grant no. IF170692), Department of Science and Technology, Government of India.

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Correspondence to Srijita Mondal.

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Mondal, S., Murmu, T., Chakravarty, K. et al. Mathematical modelling of HIV-1 transcription inhibition: a comparative study between optimal control and impulsive approach. Comp. Appl. Math. 42, 340 (2023).

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