高阶网络上具有噪声干扰的随机SIR模型研究

doi:10.6040/j.issn.1671-9352.0.2025.191

《山东大学学报(理学版)》 ›› 2026, Vol. 61 ›› Issue (7): 70-81.doi: 10.6040/j.issn.1671-9352.0.2025.191

• 生物数学 • 上一篇

高阶网络上具有噪声干扰的随机SIR模型研究

李思雨,郭祥,刘茂省^*

北京建筑大学理学院, 北京 102616

发布日期:2026-07-01
通讯作者: 刘茂省(1978— ),男,教授,博士,研究方向为生物数学. E-mail:liumaoxing@126.com
作者简介:李思雨(2001— ),女,硕士研究生,研究方向为生物数学. E-mail:lisiyu0502@163.com*通信作者:刘茂省(1978— ),男,教授,博士,研究方向为生物数学. E-mail:liumaoxing@126.com
基金资助:
国家自然科学基金项目(12071445);北京建筑大学高层次人才引进资助计划(GDRC20220802)

Study on astochastic SIR model with noise interference in higher-order networks

LI Siyu, GUO Xiang, LIU Maoxing^*

School of Science, Beijing University of Civil Engineering and Architecture, Beijing 102616, China

Published:2026-07-01

摘要/Abstract

摘要： 为了研究随机噪声对高阶网络上传染病传播的影响,本文提出了一个单纯复形网络上的随机SIR传染病模型。首先利用单纯复形构造一个描述节点间联系的社会网络,用平均场方法来描述网络中节点随时间的演化,并对传播过程施加白噪声干扰。其次通过动力学分析,得到疾病暴发的阈值,证明在一定条件下系统全局正解的存在性和唯一性、疾病的灭绝性和解的渐近振荡。最后在两个真实的网络上对该模型进行了仿真模拟,验证噪声强度对疾病传播的影响,但不同特征的网络结构对疾病传播过程有不同的影响,1-单纯形的平均度较高时疾病传播的会更快。

关键词: 单纯复形, 白噪声, 暴发阈值, Lyapunov方法

Abstract: To explore how random noise affects the spread of infectious diseases in higher-order networks, this study develops a stochastic SIR epidemic model rooted in simplicial complexes. Firstly, the model constructs a social network of node connections using simplicial complexes, leverages mean field theory to model the temporal evolution of network nodes, and integrates white noise perturbations into the transmission dynamics. Then, through dynamic analysis, the disease outbreak threshold is deduced, establishing the existence and uniqueness of the systems global positive solution under specific conditions, alongside proving disease extinction and asymptotic oscillations of the solution. Finally, simulations on two real-world networks confirm the role of noise intensity in disease spread. Critically, networks with differing topological properties exert distinct influences on transmission: higher average degrees of simplices expedite disease propagation.

Key words: simplicial complex, white noise, outbreak threshold, Lyapunov method

中图分类号:

O175

李思雨,郭祥,刘茂省. 高阶网络上具有噪声干扰的随机SIR模型研究[J]. 《山东大学学报(理学版)》, 2026, 61(7): 70-81.

LI Siyu, GUO Xiang, LIU Maoxing. Study on astochastic SIR model with noise interference in higher-order networks[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2026, 61(7): 70-81.

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高阶网络上具有噪声干扰的随机SIR模型研究

Study on astochastic SIR model with noise interference in higher-order networks

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