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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2026, Vol. 43 ›› Issue (1): 63-76.doi: 10.3969/j.issn.1005-3085.2026.01.004cstr: 32411.14.cjem.CN61-1269/O1.2026.01.004

• • 上一篇    下一篇

基于图论方法的多权重网络上随机SAIS模型指数稳定性分析

弋  鑫1,  刘桂荣2,3   

  1. 1. 太原师范学院数学与统计学院，晋中 030619

    2. 山西大学数学科学学院，太原 030006

    3. 山西大学复杂系统与数据科学教育部重点实验室，太原 030006
  • 收稿日期:2024-08-26 接受日期:2025-01-04 出版日期:2026-02-15 发布日期:2026-04-15
  • 基金资助:
    国家自然科学基金 (12371494; 12231012; 11971279)；山西省重点研发计划 (202202020101010)；山西省高等学校科技创新计划 (2024L298).

Exponential Stability of Stochastic SAIS Model with Multiple Weighted Networks on Graph-theoretical Method

YI Xin1,  LIU Guirong2,3   

  1. 1. School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong 030619
    2. School of Mathematical Sciences, Shanxi University, Taiyuan 030006
    3. Key Laboratory of Complex Systems and Data Science of Ministry of Education, Shanxi University, Taiyuan 030006
  • Received:2024-08-26 Accepted:2025-01-04 Online:2026-02-15 Published:2026-04-15
  • Supported by:
    The National Natural Science Foundation of China (12371494; 12231012; 11971279); the Key Research and Development Plan of Shanxi Province (202202020101010); the Scientific and Technological Innovation Programs of Higher Education Institutions in Shanxi (2024L298).

摘要：

研究了一类多权重复杂网络上具有意识衰减和人口异质性的随机SAIS传染病模型。利用图论的Kirchhoff矩阵树定理以及随机稳定性理论，将节点系统的Lyapunov函数和网络拓扑结构结合，构建多权重复杂网络的全局Lyapunov函数，给出了系统零解$p$阶矩指数稳定的充分条件。基于Erd$\rm{\ddot{o}}$s-R$\rm{\acute{e}}$yni随机网络和WS小世界网络，通过数值仿真验证理论结果。

关键词: 随机传染病模型, 多权重复杂网络, Kirchhoff矩阵树定理, Lyapunov函数, 指数稳定性

Abstract:

In this paper, a stochastic SAIS epidemic dynamic model on complex networks with multi-weights is discussed. According to Kirchhoff's matrix-tree theorem in graph theory and stochastic stability theory, and combining Lyapunov functions for each vertex system with network topology structure, a global Lyapunov function for complex networks with multi-weights is constructed. And then, the sufficient conditions of $p$-th moment exponential stability are further given. Based on the Erd$\rm{\ddot{o}}$s-R$\rm{\acute{e}}$yni random graph and WS small-world network, the numerical simulations validate our conclusions.

Key words: stochastic epidemic model, complex networks with multi-weights, Kirchhoff's matrix-tree theorem, Lyapunov function, exponential stability

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