乙肝病毒动力学模型的全局稳定性分析
Global Stability Analysis of a Hepatitis B Epidemic Model
摘要: 本文研究了乙肝病毒在人群中的传播过程，并深入分析了乙肝病毒携带者对传播动力学的影响。我们构建了一个具有常数输入和乙肝病毒携带者的SEAICR传染病动力学模型。通过采用下一代矩阵方法，我们计算出了模型的基本再生数，并且证明了模型平衡点的存在唯一性。进一步地，通过Routh-Hurwitz判据、Castillo-Chavez稳定性准则与LaSalle不变性原理，证明了当R0<1时，无病平衡点全局渐近稳定；当R0>1时，无病平衡点不稳定，地方病平衡点全局渐近稳定。
Abstract: This study explores the transmission process of the hepatitis B virus in the population and provides a thorough analysis of the impact of hepatitis B carriers on transmission dynamics. We constructed a SEAICR infectious disease dynamics model with constant input and incorporated hepatitis B car-riers. Using the next-generation matrix method, we calculated the basic reproduction number of the model and demonstrated the existence and uniqueness of equilibrium points. Furthermore, through the Routh-Hurwitz criterion, the Castillo-Chavez stability criterion, and the LaSalle invari-ance principle, we have established that under R0<1 , the disease-free equilibrium point exhibits global asymptotic stability, whereas under R0> , it becomes unstable, with the local disease equi-librium point attaining global asymptotic stability.
文章引用：戴乙梦, 胡绿荷, 吕贵臣. 乙肝病毒动力学模型的全局稳定性分析[J]. 应用数学进展, 2023, 12(12): 5137-5146. https://doi.org/10.12677/AAM.2023.1212504

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