Fractal scale-free networks resistant to disease spread
  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. 
Zhongzhi Zhang, Shuigeng Zhou, Zou Tao, and Guisheng Chen