In this paper, we propose a fractional optimal control model of anti-HBV infection based on saturation incidence and logistic proliferation of uninfected cells for the first time. We derive the basic reproduction number and the cytotoxic T lymphocyte immune response reproductive number and give the stable analysis based on and . We analyse the optimal control condition and give two optimal control strategies about entecavir monotherapy and combination therapy of traditional Chinese medicine and entecavir with different fractional orders by simulation. The simulation shows that combination therapy may be a good choice in anti-HBV infection therapy. We also compare the objective function values of the optimal control strategies with other constant control strategies; the comparison shows that the optimal therapy can get similar or better treatment effect with less drug dose and side effects.

中文翻译：

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HBV分数阶最优控制模型的分析与仿真

在本文中，我们首次提出了基于未感染细胞的饱和度发生率和对数增殖的抗HBV感染的最优控制模型。我们得出的基本再生数和细胞毒性T淋巴细胞的免疫应答生育数量和给出了基于稳定分析和。我们通过模拟分析了最佳控制条件，并给出了恩替卡韦单药治疗和中药与恩替卡韦联合治疗不同分数阶的两种最优控制策略。仿真表明，联合治疗可能是抗HBV感染治疗的好选择。我们还将最佳控制策略的目标函数值与其他恒定控制策略进行比较；比较结果表明，最佳治疗方案在减少药物剂量和副作用的同时，可获得相似或更好的治疗效果。