Despite many approaches to treat HIV virus, the endeavor, due to the inability of therapy to eradicate HIV infection, has been aroused to formulate rational therapeutic strategies to establish sustained immunity to suppress viruses after stopping therapy. In this paper, incorporating the time lag of the expansion of immune cells, we propose an explicit model with continuous antiretroviral therapy (CATT) and an intermittent immunotherapy to describe an interaction of uninfected cells, HIV virus and immune response. Two kinds of bistability and the sensitivities of the amplitude and period of the periodic solution with respect to all of parameters indicate that both ε and b relating to the therapy are scheduled to propose an optimal treatment tactics. Furthermore, taking a patient performed a CATT but with an unsuccessful outcome as a example, we inset a phased immunotherapy into the above CATT and then adjust the therapeutic session as well as the inlaid time to quest the preferable therapeutic regimen. Mathematically, we alter the solution of system from the basin of the attraction of the immune-free equilibrium to the immune control balance when the treatment is ceased, meanwhile minimize the cost function through a period of combined therapy. Due to the particularity of our optimal problem, we contribute a novel optimization approach by meshing a special domain on the antiretroviral and immunotherapy parameters ε and b, to catch an optimal combined treatment scheme. Simulations exhibit that early mediating immunotherapy suppresses the load of virus lower while shortening the combined treatment session does not reduce but magnify the cost function. Our results can provide some insights into the design of optimal therapeutic strategies to boost sustained immunity to quell viruses.

中文翻译：

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通过将阶段性免疫疗法与持续的抗病毒疗法相结合来增强针对HIV的免疫力和抑制病毒的最佳方案

尽管有许多治疗HIV病毒的方法，但由于无法根除HIV感染的治疗方法，已引起人们的努力以制定合理的治疗策略，以建立持续的免疫力，以在停止治疗后抑制病毒。在本文中，结合免疫细胞扩增的时滞，我们提出了一个具有连续抗逆转录病毒疗法（CATT）和间歇免疫疗法的显式模型，以描述未感染细胞，HIV病毒和免疫反应的相互作用。相对于所有参数的两种双稳态和周期解的振幅和周期的敏感性表明，ε和b与治疗有关的疾病计划提出一种最佳治疗策略。此外，以患者执行了CATT但未成功的结果为例，我们在上述CATT中插入了阶段性免疫疗法，然后调整治疗疗程以及所需的治疗时间，以寻求更好的治疗方案。在数学上，当停止治疗时，我们将系统的解决方案从无免疫平衡的吸引力转向免疫控制的平衡，同时通过一段时间的联合治疗使成本函数最小化。由于我们最优问题的特殊性，我们通过在抗逆转录病毒和免疫疗法参数ε和b上划分一个特殊的域来贡献一种新颖的优化方法，以获取最佳的组合治疗方案。模拟表明，早期介导的免疫疗法可降低病毒载量，同时缩短联合治疗时间并不会减少但会增加成本功能。我们的结果可以为优化治疗策略的设计提供一些见识，以增强对克尔病毒的持续免疫力。