In clinical practice, many cirrhosis scores based on alanine aminotransferase (ALT) levels exist. Although the most recent direct acting antivirals (DAAs) reduce fibrosis and ALT levels, the Hepatitis C virus (HCV) is not always removed. In this paper, we study a mathematical model of the HCV virus, which takes into account the role of the immune system, to investigate the ALT behavior during therapy. We find five equilibrium points and analyze their stability. A sufficient condition for global asymptotical stability of the infection-free equilibrium is obtained and local asymptotical stability conditions are given for the immune-free infection and cytotoxic T lymphocytes (CTL) response equilibria. The stability of the infection equilibrium with the full immune response is numerically performed.

中文翻译：

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包括丙氨酸氨基转移酶和免疫系统在内的丙型肝炎模型的一些稳定性结果

在临床实践中，存在许多基于丙氨酸氨基转移酶 (ALT) 水平的肝硬化评分。尽管最近的直接作用抗病毒药物 (DAA) 降低了纤维化和 ALT 水平，但丙型肝炎病毒 (HCV) 并不总是被清除。在本文中，我们研究了 HCV 病毒的数学模型，该模型考虑了免疫系统的作用，以研究治疗期间的 ALT 行为。我们找到五个平衡点并分析它们的稳定性。获得了无感染平衡全局渐近稳定性的充分条件，并给出了无免疫感染和细胞毒性T淋巴细胞（CTL）反应平衡的局部渐近稳定性条件。以数字方式执行具有完全免疫反应的感染平衡的稳定性。