Control of the medical treatment of AIDS

Velichenko, V. V.; Pritykin, Dmitry

doi:10.1134/s0005117906030131

Cited by 7 publications

(7 citation statements)

References 18 publications

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“…In Figure 5, we can observe a prolonged intake over time is required. The performed algorithm is stable, in fact, results do not vary with the initial values given to adjoint variables at time t 0 (as it happens for other studies of the related literature, see e.g., [19,20]). Computational time is about 15-60 min in an Intel(R) core(TM) i-7 4.700 HQ CPU, 2.40 GHz.…”

Section: Nonconcave Instancementioning

confidence: 72%

“…So that a numerical resolution turns out to be crucial in order to get some enlightening results. We formulate and apply an efficient and intuitive algorithm by combining the Forward-Backward Sweep algorithm [18][19][20][21] and a 4th order Runge-Kutta routine (see e.g., [22]). We performed several simulations and we always got a unique solution to the necessary conditions.…”

Section: Numerical Simulationsmentioning

confidence: 99%

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HIV vs. the Immune System: A Differential Game

2015

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A differential game is formulated in order to model the interaction between the immune system and the HIV virus. One player is represented by the immune system of a patient subject to a therapeutic treatment and the other player is the HIV virus. The aim of our study is to determine the optimal therapy that allows to prevent viral replication inside the body, so as to reduce the damage caused to the immune system, and allow greater survival and quality of life. We propose a model that considers all the most common classes of antiretroviral drugs taking into account different immune cells dynamics. We validate the model with numerical simulations, and determine optimal structured treatment interruption (STI) schedules for medications.

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Section: Nonconcave Instancementioning

confidence: 72%

Section: Numerical Simulationsmentioning

confidence: 99%

HIV vs. the Immune System: A Differential Game

2015

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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%

“…e majority of above-mentioned papers on the optimal anti-HIV therapy consider models with a single control, which correspond to the therapies where a single drug (a single action) is used. Very few of existing publications consider a possibility of simultaneous use of two drugs [15,20,[37][38][39][40], whereas works exploring interaction of three or more controls are rather exceptional [41,42]. On the other hand, the current anti-HIV therapy guidelines necessitate the use of the highly active antiretroviral therapy (HAART) that implies administering a combination of several (typically, three or four) antiretrovirals.…”

Section: Interaction Of Several Simultaneously Acting Controlsmentioning

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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“…[3][4][5][6][7][8][9][10][11][12][13][14][15], and bibliography therein). However, the models are complex and cannot be investigated analytically.…”

Section: Introductionmentioning

confidence: 99%

Modeling and Optimal Control for Antiretroviral Therapy

et al. 2014

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We consider a three-dimensional nonlinear control model based on the Wodarz HIV model. The model phase variables are populations of the uninfected and infected target cells and the concentration of an antiretroviral drug. The drug intake rate is assumed to be a bounded control function. An optimal control problem of minimizing the cumulative infection level (the infected cells population) on a given time interval is stated and solved, and the types of the optimal control for different model parameters are found by analytical methods. We thereby reduce the two-point boundary value problem (TPBVP) for the Pontryagin maximum principle to a problem of the finite-dimensional optimization. Numerical results are presented to illustrate the optimal solution.

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Control of the medical treatment of AIDS

Cited by 7 publications

References 18 publications

HIV vs. the Immune System: A Differential Game

HIV vs. the Immune System: A Differential Game

Optimal Controls of the Highly Active Antiretroviral Therapy

Modeling and Optimal Control for Antiretroviral Therapy

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