Metastability of the contact process on fast evolving scale-free networks

TL;DR

This paper investigates the metastability of the contact process on rapidly evolving scale-free networks, identifying conditions for long-term infection survival and extinction based on network dynamics and infection strategies.

Contribution

It introduces a new approach for analyzing the contact process on inhomogeneous, fast-evolving networks, focusing on specific kernels like factor and preferential attachment.

Findings

Fast extinction occurs when infection strategies fail.

Slow extinction dominates when certain strategies succeed.

Phase diagrams delineate regions of different infection survival behaviors.

Abstract

We study the contact process in the regime of small infection rates on finite scale-free networks with stationary dynamics based on simultaneous updating of all connections of a vertex. We allow the update rates of individual vertices to increase with the strength of a vertex, leading to a fast evolution of the network. We first develop an approach for inhomogeneous networks with general kernel and then focus on two canonical cases, the factor kernel and the preferential attachment kernel. For these specific networks we identify and analyse four possible strategies how the infection can survive for a long time. We show that there is fast extinction of the infection when neither of the strategies is successful, otherwise there is slow extinction and the most successful strategy determines the asymptotics of the metastable density as the infection rate goes to zero. We identify the domains in which these strategies dominate in terms of phase diagrams for the exponent describing the decay of the metastable density.