一类具有隔离项的传染病模型稳定性分析
Stability Analysis of a Kind of Epidemic Disease Model with Isolation Term
DOI: 10.12677/PM.2023.133070, PDF,   
作者: 尹 莎：成都理工大学数理学院，四川 成都
关键词: 基本再生数；稳定性分析；Lyapunov函数；Basic Reproduction Number； Stability Analysis； Lyapunov Function
摘要: 研究了一类具有带常规预防和隔离防护措施的传染病模型，运用下一代生成矩阵法求得系统的基本再生数并证明了平衡点的存在性，通过Hurwitz判别法得到无病平衡点与地方病平衡点的局部渐进稳定性，构造Lyapunov函数并利用Lasalle不变集原理得到平衡点全局渐近稳定的充分条件。
Abstract: A kind of infectious disease model with routine prevention and isolation protection measures is studied. The basic reproductive number of the system is obtained by the next generation matrix method and the existence of the equilibrium point is proved. The local asymptotic stability of the disease-free equilibrium point and the endemic equilibrium point was obtained by the Hurwitz dis-criminant method, the Lyapunov function is constructed and the sufficient condition for the global asymptotic stability of the equilibrium point is obtained by the Lasalle invariant set principle.
文章引用：尹莎. 一类具有隔离项的传染病模型稳定性分析[J]. 理论数学, 2023, 13(3): 649-658. https://doi.org/10.12677/PM.2023.133070

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