Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method

Taesoo Jang; Hee-Dae Kwon; Jeehyun Lee

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Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method

机译：基于共轭梯度法的HIV模型的自由终时最优控制问题

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The minimum duration of treatment periods and the optimal multidrug therapy for human immunodeficiency virus (HIV) type 1 infection are considered. We formulate an optimal tracking problem, attempting to drive the states of the model to a “healthy” steady state in which the viral load is low and the immune response is strong. We study an optimal time frame as well as HIV therapeutic strategies by analyzing the free terminal time optimal tracking control problem. The minimum duration of treatment periods and the optimal multidrug therapy are found by solving the corresponding optimality systems with the additional transversality condition for the terminal time. We demonstrate by numerical simulations that the optimal dynamic multidrug therapy can lead to the long-term control of HIV by the strong immune response after discontinuation of therapy.

机译：考虑了治疗时间的最短持续时间和针对人类免疫缺陷病毒（HIV）1型感染的最佳多药疗法。我们制定了一个最佳跟踪问题，试图将模型的状态驱动到“健康”的稳态，在该状态下病毒载量低而免疫反应强。我们通过分析免费终端时间最佳跟踪控制问题来研究最佳时间框架以及HIV治疗策略。通过在终端时间内通过附加的横向条件求解相应的最优系统，可以找到最短的治疗时间和最佳的多药治疗方法。我们通过数值模拟证明，最佳的动态多药疗法可以通过中断治疗后的强大免疫反应来导致对HIV的长期控制。

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《Bulletin of Mathematical Biology》 |2011年第10期|p.2408-2429|共22页
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Taesoo Jang; Hee-Dae Kwon; Jeehyun Lee;
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机译：共轭梯度法对终端状态约束下最优控制问题的适应性。

Free Terminal Time Optimal Control Problem of an HIV Model Based on a Conjugate Gradient Method

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