异质网络上随机 SIS 传染病模型的拟平稳分布与灭绝时间分析

数学物理学报 ›› 2026, Vol. 46 ›› Issue (5): 2003-2016.

异质网络上随机 SIS 传染病模型的拟平稳分布与灭绝时间分析

靖晓洁¹(), 刘桂荣²^,^*(), 靳祯³()

¹ 中北大学数学学院, 太原 030051
² 山西大学数学与统计学院, 太原 030006
³ 山西大学复杂系统研究所, 太原 030006

收稿日期:2025-02-21 修回日期:2026-04-27 出版日期:2026-10-26 发布日期:2026-09-07
通讯作者: 刘桂荣 E-mail:jingxiaojie@nuc.edu.cn;lgr5791@sxu.edu.cn;jinzhen@sxu.edu.cn
作者简介:靖晓洁, E-mail:jingxiaojie@nuc.edu.cn
靳祯, E-mail:jinzhen@sxu.edu.cn
基金资助:
国家自然科学基金(12501698);国家自然科学基金(12371494);国家自然科学基金(12231012);山西省基础研究计划(202403021222164);山西省重点研发计划(202202020101010)

A Stochastic SIS Epidemic Model in Heterogeneous Networks: Quasi-Stationarity and Extinction

Xiaojie Jing¹(), Guirong Liu²^,^*(), Zhen Jin³()

¹ School of Mathematics, North University of China, Taiyuan 030051
² School of Mathematics and Statistics, Shanxi University, Taiyuan 030006
³ Complex Systems Research Center, Shanxi University, Taiyuan 030006

Received:2025-02-21 Revised:2026-04-27 Online:2026-10-26 Published:2026-09-07
Contact: Guirong Liu E-mail:jingxiaojie@nuc.edu.cn;lgr5791@sxu.edu.cn;jinzhen@sxu.edu.cn
Supported by:
NSFC(12501698);NSFC(12371494);NSFC(12231012);Fundamental Research Program of Shanxi Province of China(202403021222164);Shanxi Provincial Key Research and Development Project(202202020101010)

摘要/Abstract

摘要：

该文章将矩封闭方法应用于异质网络上的 SIS 传染病模型. 在正态分布和对数正态分布的假设下, 推导了传播过程的拟平稳分布以及传染病从拟平稳状态开始的平均灭绝时间. 最后采用随机模拟, 检验矩封闭方法的近似效果. 结果表明, 拟平稳分布的近似效果与模拟数据拟合良好, 其中对数正态分布的拟合效果尤为突出.

关键词: 传染病传播, 异质网络, 拟平稳分布, 灭绝时间, 矩封闭

Abstract:

In this paper, the moment closure method is applied to the SIS epidemic model on heterogeneous networks. Assumptions of normal and log-normal distributions are made to capture the quasi-stationary behavior and the expected time to extinction of the disease starting from the quasi-stationary state. The approximate performance of the moment closure method is then tested by stochastic simulations. The results show that the approximation is in good agreement with the simulations for the quasi-stationary distribution, particularly for the log-normal distribution.

Key words: Epidemic spreading, Heterogeneous network, Quasi-stationary distribution, Time to extinction, Moment closure

中图分类号:

O175

靖晓洁, 刘桂荣, 靳祯. 异质网络上随机 SIS 传染病模型的拟平稳分布与灭绝时间分析[J]. 数学物理学报, 2026, 46(5): 2003-2016.

Xiaojie Jing, Guirong Liu, Zhen Jin. A Stochastic SIS Epidemic Model in Heterogeneous Networks: Quasi-Stationarity and Extinction[J]. Acta mathematica scientia,Series A, 2026, 46(5): 2003-2016.

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