Xiong Xiaowen, Li Yanqiu, Li Bingliang
School of Physical and Mathematical Sciences, Nanjing Tech University, Nanjing 211816, China.
Math Biosci Eng. 2021 Mar 4;18(3):2182-2205. doi: 10.3934/mbe.2021110.
In order to treat the diseases caused by hepatitis C virus (HCV) more efficiently, the concentration of HCV in blood, cells, tissues and the body has attracted widespread attention from related scholars. This paper studies a dynamic dependent HCV model (more specifically, including age structure and treatment methods model) that concludes states of infection-free and infected equilibrium. Through eigenvalue analysis and Volterra integral formula, it proves that $E_0$ is globally asymptotically stable when $\mathcal{R}<1$. After explaining the existence, uniqueness and positive properties of the solution of the system, we have proved the global asymptotic stability of $E^*$ when $\mathcal{R}>1$ by constructing a suitable Lyapunov function. Through the above proofs, it can be concluded that effective treatment measures can significantly reduce the number of HCVs, so many related researchers are aware of the importance of highly efficient nursing methods and are committed to applying relevant methods to practice.
为了为了更有效地治疗丙型肝炎病毒（HCV）引起的疾病，血液、细胞、组织和体内HCV的浓度引起了相关学者的广泛关注。本文研究了一个动态相关的HCV模型（更具体地说，包括年龄结构和治疗方法模型），该模型得出了无感染和感染平衡状态。通过特征值分析和Volterra积分公式，证明了当(\mathcal{R}<1)时(E_0)是全局渐近稳定的。在解释了系统解的存在性、唯一性和正性之后，我们通过构造一个合适的Lyapunov函数证明了当(\mathcal{R}>1)时(E^*)的全局渐近稳定性。通过上述证明，可以得出有效治疗措施可以显著减少HCV的数量，因此许多相关研究人员意识到高效护理方法的重要性，并致力于将相关方法应用于实践。
