标题:
异质群体中SIR型传染病爆发流行的标度律A Scaling Law of the SIR Outbreak Prevalence in Heterogeneous Medias
作者:
彭为花, 王家赠
关键字:
SIR型传染病, 键逾渗, 概率母函数, 标度律Susceptible-Infectious-Removed, Bond Percolation, Probability Generating Function, Scaling Law
期刊名称:
《Advances in Applied Mathematics》, Vol.5 No.4, 2016-11-30
摘要:
本文主要研究异质群体中SIR型传染病的爆发流行规模对于传播速率的标度律。这里的标度律计算是基于键逾渗的方法，它是通过一个自组织方程得到的。在爆发阈值附近，如果底层结构(用度分布来刻画)不是非常异质的话，不同底层结构下的标度律系数是等于1的。但是，对于无标度的网络，在α＞4时，此时的标度律系数也是1；但当3。
In this paper, we study the scaling law of the outbreak prevalence of susceptible-infectious-re- moved epidemic on the transmissibility. The scale of prevalence is calculated by bond percolation method, which is got through a self-consistent equation. Near the threshold region, we find that the scaling law coefficients of different media structures, which were represented by degree distributions, are equal to unity if the media is not so heterogeneous. For scale free networks, we find that when α＞4, the scaling law coefficient is 1; when 2 ; when 2 , which are bigger than one and depending on the parameter α.