弱聚类网络上SI传染病的渗流

The Percolation of SI Epidemic Models on Clustered Networks

考虑了含有3团和4团的弱聚类网络,并建立了联合分布函数,借助生成函数的方法得到任选一个节点属于连通巨片的概率以及节点属于连通片的平均规模和发生连通巨片相变的渗流阈值.同时将边渗流应用于SI传染病模型中,通过模拟分析聚类系数对染病者形成连通巨片规模大小的影响.

This paper considers a class of clustered networks which contains arbitrary 3-cliques and4-cliques,and establishes the multidimensional joint distribution function.By using the generating function to calculate the probability that one node belongs to the giant connected component（GCC）,the expected size of the connected component that one node is connected and the percolation threshold of the GCC.At the same time,this paper applys the bond percolation process to the spread of SI epidemic model.We study the effects of the global clustering coefficient on the existence of the GCC by numerical simulations.