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

作　　者：戴乙梦 胡绿荷 吕贵臣 

机构地区：[1]重庆理工大学理学院,重庆

出　　处：《应用数学进展》2023年第12期5137-5146,共10页Advances in Applied Mathematics

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R00>1时,无病平衡点不稳定,地方病平衡点全局渐近稳定。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 , 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.

关 键 词：病毒携带者 乙肝病毒动力学模型 LaSalle不变性原理 全局稳定性 

分 类 号：O17[理学—数学]