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It is generally accepted that scale-free networks is prone to epidemicspreading allowing the onset of large epidemics whatever the spreading rate ofthe infection. In the paper, we show that disease propagation may be suppressedin particular fractal scale-free networks. We first study analytically thetopological characteristics of a network model and show that it issimultaneously scale-free, highly clustered, "large-world", fractal anddisassortative. Any previous model does not have all the properties as the oneunder consideration. Then, by using the renormalization group technique weanalyze the dynamic susceptible-infected-removed (SIR) model for spreading ofinfections. Interestingly, we find the existence of an epidemic threshold, ascompared to the usual epidemic behavior without a finite threshold inuncorrelated scale-free networks. This phenomenon indicates that degreedistribution of scale-free networks does not suffice to characterize theepidemic dynamics on top of them. Our results may shed light in theunderstanding of the epidemics and other spreading phenomena on real-lifenetworks with similar structural features as the considered model.

Finite epidemic thresholds in fractal scale-free `large-world' networks