The contact process on scale-free geometric random graphs

TL;DR

This paper analyzes the contact process on scale-free geometric random graphs, providing asymptotic results for non-extinction probabilities and extinction times, which enhances understanding of epidemic dynamics on complex spatial networks.

Contribution

It introduces exact asymptotics for the contact process on a broad class of geometric scale-free graphs, including models like the age-dependent random connection model.

Findings

Exact asymptotics for non-extinction probability at small infection rates

Extinction time is exponential in the graph size for finite models

Results apply to various geometric random graph models

Abstract

We study the contact process on a class of geometric random graphs with scale-free degree distribution, defined on a Poisson point process on $\mathbb{R}^d$. This class includes the age-dependent random connection model and the soft Boolean model. In the ultrasmall regime of these random graphs we provide exact asymptotics for the non-extinction probability when the rate of infection spread is small and show for a finite version of these graphs that the extinction time is of exponential order in the size of the graph.