Aniji M, Kavitha N, Balamuralitharan S
Department of Mathematics, University College of Engineering, Rajamadam, Pattukkottai, Tamilnadu, India.
Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Tamilnadu, India.
Bound Value Probl. 2020;2020(1):80. doi: 10.1186/s13661-020-01373-w. Epub 2020 Apr 16.
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.
乙型肝炎病毒（HBV）是一种危及生命的病毒，可引发非常严重的肝脏相关疾病，它属于嗜肝DNA病毒科，具有与逆转录病毒相似的极为罕见的特性。在本文中，我们通过使用廖氏同伦分析法（LHAM）进行数学建模来分析抗病毒治疗的效果，该方法定义了靶肝细胞与HBV之间的联系。我们还通过LHAM研究基本非线性微分方程以获得半解析解。这可能是一种非常直接的方法，能提供合适的解。此外，使用李雅普诺夫函数对无病平衡点和地方病平衡点进行局部和全局稳定性分析。利用Mathematica 12软件来求解并绘制图形表示。我们还使用同一软件讨论了直至六阶近似的数值模拟和误差分析。
