Research Article Open Access

Optimal Control Techniques for the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics

Bassey Echeng Bassey 1 and Adagba Odey Henry1
  • 1 Department of Industrial Mathematics and Applied Statistics, Ebonyi State University, Abakaliki, Nigeria

Abstract

From the studies of HIV/AIDS transmission and treatment dynamicsusing mathematical modeling, literature reviews have shown that attention hadnot been given to the behavioral attitude of screen-aware infectives not readyto receive treatment, HIV-aware infectives that initiated treatment buttruncated only to resume treatment later (therapy abuse) and those onconsistent treatment protocols. Moreso, following the non-outright eradicationof the deadly HI-virus, recommendations have been geared towards exploringoptimal control theory for the maximization of healthy uninfected CD4+T-cells. Therefore, this present investigation seeks and formulated an optimalcontrol 6-Dimensional deterministic mathematical dynamic model, which accountedfor the Role of Antiretroviral Therapy (ART) abuse in the treatment dynamics ofthe HIV/AIDS epidemic. The materials and methods for this model are constitutedby a set of 6-Dimensional varying subpopulations interacting with concentratedHI-viral load. Interactions are investigated using bilinear control functions(condom use and ART) with empirically generated data. The model assumed adeterministic approach and was formulated using the fundamental theory ofdifferential equations. Theoretical optimal predictions explored classicalnumerical methods with optimal control techniques (Pontryagin's maximumprinciple in conjunction with Hessian matrix) as a basis. Numerical simulationswere conducted using in-built Runge-Kutta of the order of precision 4 in aMathcad surface. Following the derived model for both off-optimal control andonset-optimal control functions and model optimal control pair as well as model optimality system, resultsof simulations indicated that at off-optimal control function, near zeropopulation extinction was observed. From the application of optimal controlfunctions under optimal control techniques, there exists tremendousrejuvenation of susceptible populations vindicated by a reduction in the rateof ART abuse under a minimal proportion of bilinear control functions. Thestudy concluded that adopting optimal control techniques for the investigationof the role of ART abuse in HIV/AIDS treatment yield highly significantrecovery of healthy CD4+ T-Cells at minimal systemic cost whencompared with off-optimal control outcome. Therefore, the study not onlyaffirmed the vital concept of optimal control strategy but also, instituted theviability of the model. Thus, this model can be extensively used in Bio-systemand applied mathematics.

Journal of Mathematics and Statistics
Volume 18 No. 1, 2022, 176-195

DOI: https://doi.org/10.3844/jmssp.2022.176.195

Submitted On: 22 August 2022 Published On: 24 November 2022

How to Cite: Bassey , B. E. & Henry, A. O. (2022). Optimal Control Techniques for the Role of Antiretroviral Therapy (ART) Abuse in HIV/AIDS Treatment Dynamics. Journal of Mathematics and Statistics, 18(1), 176-195. https://doi.org/10.3844/jmssp.2022.176.195

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Keywords

  • Hamiltonian-Argument
  • Pontryagin’s-Maximum-Principle
  • Two-Point-Boundary-Value-Problem
  • Optimal-Control-Protocols
  • Dual-Bilinear-Control-Functions MSC (2010) 35F20, 93C15, 93A30, 49J15, 90C46