对淬火平均场方法求解爆发阈值的有效性进行分析,利用淬火平均场研究ER网络、SF网络和实证网络上的SIR传播,发现当邻接矩阵的最大特征值所对应的特征向量为非局域特征向量时,淬火平均场得到的理论阈值与真实阈值能较好地吻合;否则,理论阈值低于真实阈值。
We investigate the validation of the threshold predicated by the quenched mean-field theory. By using quenched mean-filed theory, we analyze SIR epidemic spreading models on ER networks, SF networks, and real networks. We find that when the eigenvector of the leading eigenvalue of the adjacent matrix is delocalized, the threshold predicated by this theoretical approach can basically fit its real threshold, and that once the leading eigenvector is localized, the theoretical threshold is lower than its actual threshold.
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