Multiobjective Optimal Control of HIV Dynamics

Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem (MOOCP) is proposed to maximize the CD4+ T cells population and minimize both the viral load and...

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Published in:Mathematical Problems in Engineering Vol. 2010; no. 1; pp. 532 - 560-134
Main Authors: Zarei, Hassan, Kamyad, Ali Vahidian, Effati, Sohrab
Format: Journal Article
Language:English
Published: New York Hindawi Limiteds 01.01.2010
Hindawi Publishing Corporation
John Wiley & Sons, Inc
Subjects:
Antiretroviral drugs
Control systems
Differential equations
Drug resistance
HIV
Human immunodeficiency virus
Immune system
Linear programming
Lymphocytes
Mathematical models
Mathematical problems
Multiple objective analysis
Optimal control
Optimization
Pareto optimum
Predictive control
Protease inhibitors
Studies
ISSN:1024-123X, 1563-5147
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Abstract Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem (MOOCP) is proposed to maximize the CD4+ T cells population and minimize both the viral load and drug costs. The weighted sum method is used, and continuous Pareto optimal solutions are derived by solving the corresponding optimality system. Moreover, a model predictive control (MPC) strategy is applied, with the final goal of implementing Pareto optimal structured treatment interruptions (STI) protocol. In particular, by using a fuzzy approach, the MOOCP is converted to a single-objective optimization problem to derive a Pareto optimal solution which among other Pareto optimal solutions has the best satisfaction performance. Then, by using an embedding method, the problem is transferred into a modified problem in an appropriate space in which the existence of solution is guaranteed by compactness of the space. The metamorphosed problem is approximated by a linear programming (LP) model, and a piecewise constant solution which shows the desired combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies is achieved.
AbstractList Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized, and a multiobjective optimal control problem (MOOCP) is proposed to maximize the CD4+ T cells population and minimize both the viral load and drug costs. The weighted sum method is used, and continuous Pareto optimal solutions are derived by solving the corresponding optimality system. Moreover, a model predictive control (MPC) strategy is applied, with the final goal of implementing Pareto optimal structured treatment interruptions (STI) protocol. In particular, by using a fuzzy approach, the MOOCP is converted to a single‐objective optimization problem to derive a Pareto optimal solution which among other Pareto optimal solutions has the best satisfaction performance. Then, by using an embedding method, the problem is transferred into a modified problem in an appropriate space in which the existence of solution is guaranteed by compactness of the space. The metamorphosed problem is approximated by a linear programming (LP) model, and a piecewise constant solution which shows the desired combinations of reverse transcriptase inhibitor (RTI) and protease inhibitor (PI) drug efficacies is achieved.
Author Sohrab Effati
Hassan Zarei
Ali Vahidian Kamyad
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Copyright Copyright © 2010 Hassan Zarei et al.
Copyright © 2010 Hassan Zarei et al. Hassan Zarei et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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Snippet Various aspects of the interaction of HIV with the human immune system can be modeled by a system of ordinary differential equations. This model is utilized,...
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SubjectTerms Antiretroviral drugs
Control systems
Differential equations
Drug resistance
HIV
Human immunodeficiency virus
Immune system
Linear programming
Lymphocytes
Mathematical models
Mathematical problems
Multiple objective analysis
Optimal control
Optimization
Pareto optimum
Predictive control
Protease inhibitors
Studies
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Title Multiobjective Optimal Control of HIV Dynamics
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