WIAS Preprint No. 2969, (2022)

Chase-escape in dynamic device-to-device networks


  • Hinsen, Alexander
    ORCID: 0000-0002-4212-0065
  • Jahnel, Benedikt
    ORCID: 0000-0002-4212-0065
  • Cali, Elie
  • Wary, Jean-Philippe

2020 Mathematics Subject Classification

  • 60J25 60K35 60K37


  • Cox point processes, random graphs, mobility, random waypoint model, percolation




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.

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