  In contrast to the conventional wisdom that scale-free networks are prone to
epidemic propagation, in the paper we present that disease spreading is
inhibited in fractal scale-free networks. We first propose a novel network
model and show that it simultaneously has the following rich topological
properties: scale-free degree distribution, tunable clustering coefficient,
"large-world" behavior, and fractal scaling. Existing network models do not
display these characteristics. Then, we investigate the
susceptible-infected-removed (SIR) model of the propagation of diseases in our
fractal scale-free networks by mapping it to bond percolation process. We find
an existence of nonzero tunable epidemic thresholds by making use of the
renormalization group technique, which implies that power-law degree
distribution does not suffice to characterize the epidemic dynamics on top of
scale-free networks. We argue that the epidemic dynamics are determined by the
topological properties, especially the fractality and its accompanying
"large-world" behavior.
