The Susceptible-Infected-Susceptible (SIS) model is one of the simplestmemoryless system for describing information/epidemic spreading phenomena withcompeting creation and spontaneous annihilation reactions. The effect ofquenched disorder on the dynamical behavior has recently been compared toquenched mean-field (QMF) approximations in scale-free networks. QMF can takeinto account topological heterogeneity and clustering effects of the activityin the steady state by spectral decomposition analysis of the adjacency matrix.Therefore, it can provide predictions on possible rare-region effects, thus onthe occurrence of slow dynamics. I compare QMF results of SIS with simulationson various large dimensional graphs. In particular, I show that for Erd\Hos-R\'enyi graphs this method predicts correctly the epidemic threshold and therare-region effects. Griffiths Phases emerge if the graph is fragmented or ifwe apply strong, exponentially suppressing weighting scheme on the edges. Thelatter model describes the connection time distributions in the face-to-faceexperiments. In case of generalized Barab\'asi-Albert type of networks withaging connections strong rare-region effects and numerical evidence forGriffiths Phase dynamics are shown.
展开▼
