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

TL;DR

This paper demonstrates that certain fractal scale-free 'large-world' networks can suppress epidemic spreading, showing a finite epidemic threshold unlike typical scale-free networks, due to their unique topological properties.

Contribution

The study introduces a fractal, highly clustered, disassortative scale-free network model with a finite epidemic threshold, contrasting with previous models lacking these features.

Findings

Existence of a finite epidemic threshold in the model

Network's fractal and disassortative properties influence spreading dynamics

Degree distribution alone does not determine epidemic behavior

Abstract

It is generally accepted that scale-free networks is prone to epidemic spreading allowing the onset of large epidemics whatever the spreading rate of the infection. In the paper, we show that disease propagation may be suppressed in particular fractal scale-free networks. We first study analytically the topological characteristics of a network model and show that it is simultaneously scale-free, highly clustered, "large-world", fractal and disassortative. Any previous model does not have all the properties as the one under consideration. Then, by using the renormalization group technique we analyze the dynamic susceptible-infected-removed (SIR) model for spreading of infections. Interestingly, we find the existence of an epidemic threshold, as compared to the usual epidemic behavior without a finite threshold in uncorrelated scale-free networks. This phenomenon indicates that degree distribution of scale-free networks does not suffice to characterize the epidemic dynamics on top of them. Our results may shed light in the understanding of the epidemics and other spreading phenomena on real-life networks with similar structural features as the considered model.