Six Susceptible-Infected-Susceptible Models on Scale-free Networks

TL;DR

This paper analyzes six different epidemic models on scale-free networks using degree-based mean-field theory, revealing how contact and propagation mechanisms influence the existence of outbreak thresholds.

Contribution

It introduces and compares six susceptible-infected-susceptible models, highlighting the conditions under which epidemic thresholds exist or vanish on scale-free networks.

Findings

Outbreak thresholds depend on contact and propagation mechanisms.

Some models show no epidemic threshold on scale-free networks.

The presence of thresholds varies with model specifics.

Abstract

Spreading phenomena are ubiquitous in nature and society. For example, disease, rumor, and information spread over underlying social and information networks. It is well known that there is no threshold for epidemic models on scale-free networks; this suggests that disease can spread on such networks, regardless of how low the contact rate may be. In this paper, I consider six models with different contact and propagation mechanisms. Each model is analyzed by degree-based mean-field theory. I show that the presence or absence of an outbreak threshold depends on the contact and propagation mechanism.