Free terminal time optimal control problem for the treatment of HIV infection

¹ Laboratory of Analysis, Modeling and Simulation, Department of Mathematics and Computer Science, Faculty of Sciences Ben M’sik, Hassan II University, Casablanca, Morocco

IJOCTA 2016, 6(1), 33–51; https://doi.org/10.11121/ijocta.01.2016.00270

Submitted: 1 September 2015 | Published: 27 January 2016

© 2016 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )

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Abstract

In this work, an optimal control approach is presented in order to propose an optimal therapy for the treatment HIV infection using a combination of two appropriate treatment strategies. The optimal treatment duration and the optimal medications amount are considered. The main objective of this study is to be able to maximize the benet based on number of healthy CD4+ T-cells and CTL immune cells and to minimize the infection level and the overall treatment cost while optimizing the duration of therapy. The free terminal time optimal control problem is formulated and the Pontryagin's maximum principle is employed to provide the explicit formulations of the optimal controls. The corresponding optimality system with the additional transversality condition for the terminal time is derived and solved numerically using an adapted iterative method with a Runge-Kutta fourth order scheme and a gradient method routine.

Keywords

Interleukin-2 immunotherapy; Highly active antiretroviral therapy; Pontryagin’s maximum principle; Free terminal time optimal tracking control problem

Forward backward sweep method

Conflict of interest

The authors declare they have no competing interests.

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