Chase-escape in dynamic device-to-device networks

TL;DR

This paper analyzes the conditions under which an infection persists or dies out in a mobile, multi-layer network with chase-escape dynamics, using percolation and multiscale analysis in a spatially dynamic setting.

Contribution

It extends chase-escape models to mobile, urban environments with a new multi-layer network framework and provides conditions for infection survival based on device speed.

Findings

Identifies parameter regimes for infection survival and extinction.

Provides conditions for the transition between survival and extinction regimes.

Uses percolation and multiscale analysis techniques for proofs.

Abstract

The present paper features results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in [CHJW22], we consider an urban environment, represented by line-segments in the plane, in which agents move according to a random waypoint model based on a Poisson point process. Whenever two agents are at sufficiently close proximity for a sufficiently long time the infection can be transmitted and then propagates into the system according to the same rule starting from a typical device. Inspired by wireless network architectures, the network is additionally equipped with a second class of agents that is able to transmit a patch to neighboring infected agents that in turn can further distribute the patch, leading to a chase-escape dynamics. We give conditions for parameter configurations that guarantee existence and absence of global survival as well as an in-and-out of the survival regime, depending on the speed of the devices. We also provide complementary results for the setting in which the chase-escape dynamics is defined as an independent process on the connectivity graph. The proofs mainly rest on percolation arguments via discretization and multiscale analysis.