Exponential extinction time of the contact process on rank-one inhomogeneous random graphs

TL;DR

This paper demonstrates that the contact process on certain large random graphs, including rank-one inhomogeneous and Erdős-Rényi graphs with high mean degree, persists for an exponentially long time, revealing metastable behavior.

Contribution

It establishes the exponential survival time of the contact process on these graphs and proves a metastability result for the extinction time.

Findings

Contact process survives exponentially long on large graphs

Metastable behavior of extinction time is demonstrated

Results hold for graphs with sufficiently large mean degree

Abstract

We show that the contact process on the rank-one inhomogeneous random graphs and Erdos-R{\'e}nyi graphs with mean degree large enough survives a time exponential in the size of these graphs for any positive infection rate. In addition, a metastable result for the extinction time is also proved.