https://doi.org/10.1140/epjp/s13360-024-04911-y
Regular Article
Transmission dynamics and optimal control strategies in a multi-pathways delayed HIV infection model with multi-drug therapy
1
Nopany Institute of Management Studies, 2D Nando Mullick Lane, 700006, Kolkata, India
2
Department of Mathematics, Rajiv Gandhi National Institute of Youth Development, 602105, Sriperumbudur, Tamil Nadu, India
3
Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, 700032, Kolkata, India
Received:
3
October
2023
Accepted:
16
January
2024
Published online:
3
February
2024
In this article, we develop and study an optimal control in a multi-pathways in-host HIV infection model with saturated incidence, intracellular delay, and self-proliferation of the host cells. In the first phase, all three controls are assumed to be constant; in the second phase, controls are considered time-dependent. We determine the infected steady state’s local stability conditions and discuss the delay-induced bifurcation. In the time-dependent case, we define a suitable objective function to maximize the cell counts of healthy cells. We apply Pontryagin’s minimum principle to give the conditions for optimal control. PRCC-based sensitivity analyses are performed to identify the system’s sensitive parameters and cost function. In addition, cost-effectiveness analyses are carried out to recognize the most cost-effective strategy. We validate and compare the effect of different drug therapies for various intracellular delays through numerical simulation. It is observed that the infection can be removed by all multi-drug treatments, including cell-to-cell blockers, for any delay. The cost-effectiveness analysis suggests that protease inhibitors and cell-to-cell blockers are a comparatively better strategy for relieving HIV-1 infection using a multi-drug therapeutic scheme. The study also indicates that the treatment duration depends on delay, i.e., if the delay is shorter, the treatment period is also faster.
Research is supported by CSIR, India, Ref. No. 25(0294)/18/EMR-II.
Copyright comment Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.