Journal of Applied Nonlinear Dynamics 12(1) (2023) 39--51 | DOI:10.5890/JAND.2023.03.003

Uzzwal Kumar Mallick$^{1}$, Ashrafur Rahman$^{2}$, Md. Haider Ali Biswas$^{1}$, Md. Samsuzzoha$^{3}$, Sankar Kumar Roy$^{4}$

$^{1}$ Mathematics Discipline, Khulna University, Bangladesh

$^{2}$ Department of Mathematics and Statistics, Oakland University, USA

$^{3}$ Department of Mathematics, Swinburne University of Technology, Australia

$^{4}$ Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, India

Abstract

While cure is rare, a systemic and proper treatment can prolong the lives of HIV positive individuals and keep them healthy. To reduce toxicity and minimize treatment costs an optimal treatment program is critically important. Here we present and study a mathematical model to find an optimal treatment strategy, target-oriented-treatent (TOT), against HIV infections. We highlight the optimization case when a given CD4$^+$ T cells are required in a treatment period. The model demonstrates the viral dynamics in the presence of an immune boosting nutrition and an antiretroviral drug. It is found that the infected virus particles can be made negligible if the label of CD4$^+$T cells remains non-decreasing via treatment. Unlike other studies, boundary conditions are applied on the state variables to find the optimal solution in these regard. The results are confirmed by maximizing the objective functional via Pontryagin's Maximum Principle.

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