重叠网络上信息与疾病传播模型及其分析

山东大学学报（理学版） ›› 2016, Vol. 51 ›› Issue (11): 107-114.

重叠网络上信息与疾病传播模型及其分析

梁蕾,刘桂荣^*

山西大学数学科学学院, 山西太原 030006

收稿日期:2016-02-03 出版日期:2016-11-20 发布日期:2016-11-22
通讯作者: 刘桂荣(1975— ), 男, 教授, 博导,研究方向为生物动力系统. E-mail:lgr5791@sxu.edu.cn E-mail:959882029@qq.com
作者简介:梁蕾(1990— ), 女, 硕士研究生, 研究方向为微分方程与动力系统. E-mail:959882029@qq.com
基金资助:
国家自然科学基金资助项目(11471197);山西省自然科学基金资助项目(2014011005-1)

Analysis of an epidemic model with information on overlay network

LIANG Lei, LIU Gui-rong^*

School of Mathematical Sciences, Shanxi University, Taiyuan 030006, Shanxi, China

Received:2016-02-03 Online:2016-11-20 Published:2016-11-22

摘要/Abstract

摘要： 建立了重叠网络上的SAIS模型, 应用泰勒公式以及矩阵理论, 得到疾病传染强度的第二阈值的表达式。进一步通过数值模拟和随机模拟比较可知, 信息的传播抑制了疾病的传播, 且染病者恢复后形成的警觉性会增大疾病传染强度的第二阈值, 并有效降低疾病的传播规模。

关键词: 重叠网络, 信息传播, 传染强度, SAIS模型, 阈值

Abstract: An SAIS model on overlay network is established. Using the Taylors formula and Matrix theory, the expression of the second threshold of infection strength is obtained. Furthermore, by comparing the numerical simulations and stochastic simulations it can be found that the dissemination of information inhibits the epidemic spreading, and the alertness of recovery increases the second epidemic threshold of infection strength, also effectively reduces the infection size.

Key words: overlay network, infection strength, information dissemination, threshold, SAIS model

中图分类号:

O175

梁蕾,刘桂荣. 重叠网络上信息与疾病传播模型及其分析[J]. 山东大学学报（理学版）, 2016, 51(11): 107-114.

LIANG Lei, LIU Gui-rong. Analysis of an epidemic model with information on overlay network[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(11): 107-114.

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