Fractal scale-free networks resistant to disease spread

Abstract

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.

13 pages, 4 figures

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• Mean first-passage time for random walks on the T-graph
• Distinct scalings for mean first-passage time of random walks on scale-free networks with the same degree sequence
• Anomalous behavior of trapping on a fractal scale-free network
• Different thresholds of bond percolation in scale-free networks with identical degree sequence
• Multifractality in random networks with power-law decaying bond strengths
• Structural and spectral properties of a family of deterministic recursive trees: Rigorous solutions
• The rigorous solution for the average distance of a Sierpinski network
• Effects of node position on diffusion and trapping efficiency for random walks on fractal scale-free trees
• Organization of cooperation in fractal structures
• Universality classes in the time evolution of epidemic outbreaks on complex networks