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Chase–escape in dynamic device-to-device networks

Part of: Markov processes Special processes

Published online by Cambridge University Press:  07 August 2023

Elie Cali ,
Alexander Hinsen ,
Benedikt Jahnel  and
Jean-Philippe Wary
Elie Cali*
Affiliation:
Orange S.A.
Alexander Hinsen*
Affiliation:
Weierstrass Institute Berlin
Benedikt Jahnel*
Affiliation:
Weierstrass Institute Berlin & Technische Universität Braunschweig
Jean-Philippe Wary*
Affiliation:
Orange S.A.
*
*Postal address: Orange Labs, 44 Avenue de la République, 92320 Châtillon, France.
***Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany.
***Postal address: Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstraße 39, 10117 Berlin, Germany.
*Postal address: Orange Labs, 44 Avenue de la République, 92320 Châtillon, France.
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Abstract

We feature results on global survival and extinction of an infection in a multi-layer network of mobile agents. Expanding on a model first presented in Cali et al. (2022), 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 able to transmit a patch to neighboring infected agents that in turn can further distribute the patch, leading to 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.

Keywords

Random segment processPoisson point processCox point processrandom waypoint modelcontinuum percolationgeostatistical Boolean modelnon-Markovian dynamics

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory 60K37: Processes in random environments
Secondary: 60J25: Continuous-time Markov processes on general state spaces
Type
Original Article
Information
Journal of Applied Probability , Volume 61 , Issue 1 , March 2024 , pp. 311 - 339
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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