Super-exponential extinction time of the contact process on random geometric graphs

TL;DR

This paper establishes that the contact process on random geometric graphs with increasing connection radius persists for a super-exponentially long time, regardless of the infection rate, highlighting extreme resilience in such networks.

Contribution

It provides new bounds demonstrating super-exponential survival times of the contact process on these graphs as the connection radius grows.

Findings

Contact process survives super-exponentially long times

Survival time bounds are established for large connection radii

Results hold for any infection rate 5 > 0

Abstract

In this paper, we prove lower and upper bounds for the extinction time of the contact process on random geometric graphs with connecting radius tending to infinity. We obtain that for any infection rate $\lambda >0$, the contact process on these graphs survives a time super-exponential in the number of vertices.