Epidemic Threshold of Susceptible-Infected-Susceptible Model on Complex Networks

TL;DR

This paper investigates the epidemic threshold of the SIS model on complex networks, revealing an inactive Griffiths phase due to fluctuations, contrasting with mean field predictions, and proposes a percolation-based approach supported by numerical studies.

Contribution

It introduces the concept of an inactive Griffiths phase in the SIS model on complex networks and links the epidemic threshold to percolation thresholds through numerical analysis.

Findings

Identification of an inactive Griffiths phase in SIS dynamics.

Contradiction of mean field theory predictions.

Connection between epidemic threshold and percolation threshold.

Abstract

We demonstrate that the susceptible-infected-susceptible (SIS) model on complex networks can have an inactive Griffiths phase characterized by a slow relaxation dynamics. It contrasts with the mean field theoretical prediction that the SIS model on complex networks is active at any nonzero infection rate. The dynamic fluctuation of infected nodes, ignored in the mean field approach, is responsible for the inactive phase. It is proposed that the question whether the epidemic threshold of the SIS model on complex networks is zero or not can be resolved by the percolation threshold in a model where nodes are occupied in the degree-descending order. Our arguments are supported by the numerical studies on scale-free network models.