加权网络上一类SIRS传染病模型的动力学分析
Dynamics Analysis of an SIRS Epidemic Model on Weighted Networks
DOI: 10.12677/AAM.2019.83042, PDF,    科研立项经费支持
作者: 袁叙普, 胡海军：长沙理工大学数学与统计学院，湖南 长沙；李 娟：
关键词: SIRS模型；权重网络；全局渐近稳定；准持久；SIRS Epidemic Model； Weighted Networks； Globally Asymptotically Stable； Quasi-Persistent
摘要: 本文主要研究基于权重网络的一类SIRS传染病模型的动力学行为，发现基本再生数R0决定了传染疾病的传播与否。即，若R0<1则无病平衡点E0是全局渐近稳定性的；若R0>1则地方病平衡点E*是存在唯一的，并且此时系统也是准持久的。最后通过数值仿真，验证了理论结果的正确性。
Abstract: In this paper, an improved SIRS epidemic model on weighted networks is investigated and we ob-tain that the basic reproduction number R0 determines whether a disease persists, i.e., if R0<1, then the disease-free equilibrium E0 is globally asymptotically stable; if R0>1, there exists a unique endemic equilibrium E*. Furthermore, the model is quasi-persistent if R0>1. Finally, some simulations are presented to demonstrate the correctness of the theoretical results.
文章引用：袁叙普, 胡海军, 李娟. 加权网络上一类SIRS传染病模型的动力学分析[J]. 应用数学进展, 2019, 8(3): 371-380. https://doi.org/10.12677/AAM.2019.83042

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