{
  "id": "1805.05034",
  "version": "v1",
  "published": "2018-05-14T07:35:05.000Z",
  "updated": "2018-05-14T07:35:05.000Z",
  "title": "A stochastic SIR model on a graph with epidemiological and population dynamics occurring over the same time scale",
  "authors": [
    "Pierre Montagnon"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "We define and study an open stochastic SIR model on a graph in order to describe the spread of an epidemic on a cattle trade network with epidemiological and demographic dynamics occurring over the same time scale. Entries are assumed to be density-dependent with a constant component, the amplitude of which determines the overall scale of the population process. Standard branching approximation results for the epidemic process are first given, along with a numerical computation method for the probability of a major epidemic outbreak. This procedure is illustrated using real data on trade-related cattle movements from a densely populated livestock faming region in western France (Finist\\`ere) and epidemiological parameters corresponding to an infectious epizootic disease. In a second time, we exhibit an exponential lower bound for the total size of the epidemic in the stable endemic case as a scaling parameter goes to infinity using the Freidlin-Wentzell theory of large deviations from a dynamical system.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-14T07:35:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "time scale",
      "population dynamics occurring",
      "populated livestock faming region",
      "open stochastic sir model",
      "epidemiological"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}