The main aim of this study is to analyze the dynamical properties of hepatitis B‐type virus (HBV) infection in terms of mathematical model. The presented mathematical model on HBV involves the various factors such as immune impairment, total carrying capacity, logistic growth term, and antiretroviral therapies. In addition, the effect of time delays is also considered into the model, which are inevitable during the activation of immune response and time taken to infect the healthy cells. Mathematically, the qualitative analyses such as stability, bifurcation, and stabilization analysis are performed to explore the dynamical characteristics of HBV over the period of time. The significance of the model parameters is revealed through Hopf‐type bifurcation analysis and the global stability analysis of the proposed model. With the help of data set values that are extracted from the literature, the efficiency of the derived theoretical results is explored.

中文翻译：

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乙型肝炎病毒感染模型的稳定性和分叉性分析

这项研究的主要目的是根据数学模型分析乙型肝炎病毒（HBV）感染的动力学特性。所提出的HBV数学模型涉及各种因素，例如免疫损伤，总携带能力，逻辑增长期和抗逆转录病毒疗法。另外，在模型中还考虑了时间延迟的影响，这在免疫应答激活和感染健康细胞所花费的时间中是不可避免的。在数学上，进行了稳定性，分叉和稳定性分析等定性分析，以探索一段时间内HBV的动力学特征。通过Hopf型分叉分析和所提出模型的整体稳定性分析，揭示了模型参数的重要性。