Hepatitis B virus (HBV) is a life-threatening virus that causes very serious liver-related diseases from the family of Hepadnaviridae having very rare qualities resembling retroviruses. In this paper, we analyze the effect of antiviral therapy through mathematical modeling by using Liao’s homotopy analysis method (LHAM) that defines the connection between the target liver cells and the HBV. We also examine the basic nonlinear differential equation by LHAM to get a semi-analytical solution. This can be a very straight and direct method which provides the appropriate solution. Moreover, the local and global stability analysis of disease-free and endemic equilibrium is done using Lyapunov function. Mathematica 12 software is used to find out the solutions and graphical representations. We also discuss the numerical simulations up to sixth-order approximation and error analysis using the same software.

中文翻译：

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抗病毒治疗期间使用LHAM进行稳定性分析的HBV感染的近似解决方案

乙型肝炎病毒（HBV）是一种威胁生命的病毒，可引起来自嗜肝病毒科的非常严重的肝脏相关疾病，其质量与逆转录病毒相似，非常罕见。在本文中，我们通过使用辽氏同型分析方法（LHAM）定义了目标肝细胞与HBV之间的联系，通过数学模型分析了抗病毒治疗的效果。我们还研究了LHAM的基本非线性微分方程，以得到半解析解。这可以是一种非常直接的方法，可以提供适当的解决方案。此外，使用Lyapunov函数对无病和地方病平衡进行局部和全局稳定性分析。Mathematica 12软件用于查找解决方案和图形表示。