{
  "id": "2211.05476",
  "version": "v1",
  "published": "2022-11-10T10:44:37.000Z",
  "updated": "2022-11-10T10:44:37.000Z",
  "title": "Chase-escape in dynamic device-to-device networks",
  "authors": [
    "Elie Cali",
    "Alexander Hinsen",
    "Benedikt Jahnel",
    "Jean-Philippe Wary"
  ],
  "comment": "20 pages, 5 figures",
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-10T10:44:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J25",
      "60K35",
      "60K37"
    ],
    "keywords": [
      "dynamic device-to-device networks",
      "global survival",
      "chase-escape dynamics",
      "paper features results",
      "random waypoint model"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}