  The Susceptible-Infected-Susceptible (SIS) model is one of the simplest
memoryless system for describing information/epidemic spreading phenomena with
competing creation and spontaneous annihilation reactions. The effect of
quenched disorder on the dynamical behavior has recently been compared to
quenched mean-field (QMF) approximations in scale-free networks. QMF can take
into account topological heterogeneity and clustering effects of the activity
in the steady state by spectral decomposition analysis of the adjacency matrix.
Therefore, it can provide predictions on possible rare-region effects, thus on
the occurrence of slow dynamics. I compare QMF results of SIS with simulations
on various large dimensional graphs. In particular, I show that for Erd\H
os-R\'enyi graphs this method predicts correctly the epidemic threshold and the
rare-region effects. Griffiths Phases emerge if the graph is fragmented or if
we apply strong, exponentially suppressing weighting scheme on the edges. The
latter model describes the connection time distributions in the face-to-face
experiments. In case of generalized Barab\'asi-Albert type of networks with
aging connections strong rare-region effects and numerical evidence for
Griffiths Phase dynamics are shown.
