Fractal scale-free networks resistant to disease spread

Abstract

The conventional wisdom is that scale-free networks are prone to epidemic propagation; inthe paper we demonstrate that, on the contrary, disease spreading is inhibited in fractalscale-free networks. We first propose a novel network model and show that itsimultaneously has the following rich topological properties: scale-free degree distribution,tunable clustering coefficient, ‘large-world’ behavior, and fractal scaling. Existingnetwork models do not display these characteristics. Then, we investigate thesusceptible–infected–removed (SIR) model of the propagation of diseases in ourfractal scale-free networks by mapping it to the bond percolation process. Weestablish the existence of non-zero tunable epidemic thresholds by making useof the renormalization group technique, which implies that power law degreedistribution does not suffice to characterize the epidemic dynamics on top of scale-freenetworks. We argue that the epidemic dynamics are determined by the topologicalproperties, especially the fractality and its accompanying ‘large-world’ behavior.