异质底层结构对SIR型传播的两面性影响:阈值和爆发规模(英文)  

Dual Effects of Heterogeneous Infrastructure on SIR Epidemics:Threshold and Outbreak Size

作　　者：王家赠[1] 

机构地区：[1]北京工商大学数学系,北京100048

出　　处：《数学进展》2012年第5期615-634,共20页Advances in Mathematics（China）

基　　金：supported by NSFC(No.11001004);Beijing Municipal Government Foundation for Talents(No.2011D005003000009)

摘　　要：本文的主要目的是研究底层结构对易感一得病—移除(SIR)型传播的影响.除了周知的阈值决定因素λc=〈k^2〉/〈k〉之外,本文发现另一个看起来矛盾的现象:当传染率λ超过阈值λc后,异质结构对于传播具有消极影响.本文对机制作了定量的解释.更进一步,本文引进了"合作性"的概念,来测量异质性对于爆发规模的总体影响,发现"合作性"负相关于底层结构度分布的变异系数.这个结果说明,底层结构的异质性在疾病的开始阶段和传播阶段有不同的作用模式.The main purpose of this paper is to investigate the effects of infrastructure on the susceptible-infectious-removed（SIR） epidemic dynamics. In addition to the well-known determination of the threshold of transmission intensity λc =（k^2）/（k） there is another seemingly discrepant phenomenon： the heterogeneity has negative influence on the outbreak size of SIR epidemic when λ exceeds the threshold λc. The underlying mechanism is explained quantitatively. Furthermore, we adopt the concept of ＂cooperativity＂ to measure the overall effects of the heterogeneity after outbreak, find that it is negatively related to the coefficient of variation（CV）： the ratio of standard deviation to mean. These results tell us that the role played by heterogeneity at the starting point of epidemic, which determines the outbreak threshold, is different from that in the course of the propagation.

关 键 词：爆发阈值 得病率 变异系数 再生数 合作性 

分 类 号：O211.6[理学—概率论与数理统计]