摘要
概述了用复杂网络的理论来研究两个传染病模型,即SIR模型和SIS模型,以及在这两个模型中如何计算疾病的传播阈值。由复杂网络的局部渐近性质———在图中节点的总个数趋于∞时,图具有局部树形结构,可知SIR模型可以用分支过程理论来研究,从而根据母函数的方法可得到一些很好的性质。而SIS模型可以通过平均场的理论得以理解,且知不论在度相关Scale-Free网络中还是度不相关Scale-Free网络中都不存在非零传播阈值。
In this paper we review briefly the recent discussion in literature about the two infectious diseases models：SIR model and SIS model and the problem of how to calculate the transmission threshold in value of the two models. According to the local asymptotic properties of complex networks,when the pitch point number in the graph goes to infinity, the graph is locally shaped into a tree-like stucture. SIR model can be studied using the theory of branching process . It leads to get some good properties by using the method of generating functions. SIS model can be understood by the mean field theory, and whether in degree correlated Scale-Free networks or in degree uncorrelated Scale-Free networks, there does not exist nonzero transmission threshold.
出处
《重庆师范大学学报（自然科学版）》
CAS
2005年第4期1-5,共5页
Journal of Chongqing Normal University:Natural Science
基金
国家自然科学基金重点项目(No.10531070)
关键词
复杂网络
度分布
渗流
传播阈值
complex networks
degree distribution
percolation
transmission threshold
