A controlled treatment strategy applied to HIV immunology model

Ahmed, Shohel; Alim, Abdul; Sumaiya, Rahman

doi:10.3934/naco.2018019

Cited by 2 publications

(2 citation statements)

References 18 publications

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“…e problem of HIV control and the applicability of the optimal control theory to this problem attracted attention of mathematicians fairly early: seminal works by Butler et al [7] and Kirschner et al [8] initiated extensive literature in this direction. A mathematical techniques suggested in these publications proved to be successful and was subsequently applied to a variety of mathematical model of HIV (see, e.g., [9][10][11][12][13][14][15][16][17][18][19][20][21][22] and bibliography therein). ese results brought important insight into the problem.…”

Section: Antiretroviral Drugs and Guidelinesmentioning

confidence: 99%

Optimal Controls of the Highly Active Antiretroviral Therapy

Grigorieva

Хайлов

Korobeinikov

2020

Abstract and Applied Analysis

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In this paper, we study generic properties of the optimal, in a certain sense, highly active antiretroviral therapy (or HAART). To address this problem, we consider a control model based on the 3-dimensional Nowak–May within-host HIV dynamics model. Taking into consideration that precise forms of functional responses are usually unknown, we introduce into this model a nonlinear incidence rate of a rather general form given by an unspecified function of the susceptible cells and free virus particles. We also add a term responsible to the loss of free virions due to infection of the target cells. To mirror the idea of highly active anti-HIV therapy, in this model we assume six controls that can act simultaneously. These six controls affecting different stage of virus life cycle comprise all controls possible for this model and account for all feasible actions of the existing anti-HIV drugs. With this control model, we consider an optimal control problem of minimizing the infection level at the end of a given time interval. Using an analytical mathematical technique, we prove that the optimal controls are bang-bang, find accurate estimates for the maximal possible number of switchings of these controls and establish qualitative types of the optimal controls as well as mutual relationships between them. Having the estimate for the number of switchings found, we can reduce the two-point boundary value problem for Pontryagin Maximum Principle to a considerably simpler problem of the finite-dimensional optimization, which can be solved numerically. Despite this possibility, the obtained theoretical results are illustrated by numerical calculations using BOCOP–2.0.5 software package, and the corresponding conclusions are made.

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Section: Antiretroviral Drugs and Guidelinesmentioning

confidence: 99%

Optimal Controls of the Highly Active Antiretroviral Therapy

Grigorieva

Хайлов

Korobeinikov

2020

Abstract and Applied Analysis

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“…Since too large dosage may not be desirable for patients while too small dosage may be ineffective as therapy for the recommended therapeutic agents. Hence, mathematical modelling of optimal control theory has been considered important in a long-standing application in HIV treatment strategies ( Adams et al., 2005 ; Ahmed et al., 2018 ; Butler et al., 1997 ; Hattaf & Yousfi, 2012 ; Joshi, 2002 ; Kirschner et al., 1997 ; Ogunlaran & Oukouomi Noutchie, 2016 ; Zhou et al., 2014 ). The basic viral infection model consists of three dynamical components including the uninfected cells, the infected cells, and the free viruses was first studied in ( Nowak & May 2000 ).…”

Section: Introductionmentioning

confidence: 99%

Optimal treatment strategies to control acute HIV infection

Ahmed

Rahman

Kamrujjaman

2021

Infectious Disease Modelling

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Various antiretroviral therapies (ART) are administered to symptomatic human immunodeficiency virus (HIV) infected individuals to improve their health. The treatment effectiveness may depend on suppressing development of drug resistance, reduce evolution of new viral strains, minimize serious side effects and the costs of drugs. This paper deals with some results concerning optimal drug administration scheme successful in improving patients' health especially in poorly resourced settings. The model under consideration describes the interaction between the uninfected cells, the latently infected cells, the productively infected cells, and the free viruses. Generally, in viral infection, the drug strategy aspects either the virus infectivity or reduce the virion production. The mathematical model proposed here, deals with both situations with the objective function based on a combination of maximizing benefit relied on T cells count (the white cells that coordinate activities of the immune system) and minimizing the systemic cost. The existence of the optimal control pair is established and the Pontryagin's minimum principle is used to characterize these two optimal controls. The optimality system is derived and solved numerically using the forward and backward sweep method (FBSM). Our results indicate that early initiation of treatment makes a profound impact in both improving the quality of life and reducing the economic costs of therapy.

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A controlled treatment strategy applied to HIV immunology model

Cited by 2 publications

References 18 publications

Optimal Controls of the Highly Active Antiretroviral Therapy

Optimal Controls of the Highly Active Antiretroviral Therapy

Optimal treatment strategies to control acute HIV infection

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