一类具有断边重连的SIR网络疾病模型的传播动力学  

Transmission Dynamics of SIR Model with Rewiring on Configuration Network

作　　者：高书飞 原三领[1] GAO Shu-fei;YUAN San-ling(College of Science,University of Shanghai for Science and Technology,Shanghai 200093 China)

机构地区：[1]上海理工大学理学院,上海200093

出　　处：《生物数学学报》2019年第2期282-288,共7页Journal of Biomathematics

基　　金：国家自然科学基金项目(11671260).

摘　　要：考虑到疾病传播中邻居关系的快速改变和异质性,本文在具有配置结构的网络上建立了一类基于边且具有断边重连的SIR网络模型.首先得到了确定疾病在网络上能否流行的阈值条件,即基本再生数:当基本再生数不大于1时,模型存在唯一稳定的无病平衡点;当基本再生数大于1时,无病平衡点失稳,此时模型存在一个稳定的地方病平衡点.进而得到了疾病最终流行规模.数值模拟结果显示模型的解与100次随机模拟结果的均值能够很好地吻合.Considering the rapid change and heterogeneity of partnerships in disease transmission,in this paper,an edge-based SIR model with rewiring is developed on configuration network.Firstly,the threshold condition to determine whether the disease can be spread on the network is obtained,i.e.,the basic reproduction number:When the basic reproduction number is less than 1,the model has a unique and stable disease-free equilibrium point;When the basic reproduction number is greater than 1,the disease-free equilibrium point becomes unstable and emerges a stable endemic equilibrium point.The numerical simulation results show that the solution of the model is in good agreement with the mean value of 100 random simulation results.

关 键 词：SIR模型 配置网络 平均场 断边重连 基本再生数 疾病流行规模 

分 类 号：R181[医药卫生—流行病学] O157.5[医药卫生—公共卫生与预防医学]