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