{
  "id": "1901.06568",
  "version": "v1",
  "published": "2019-01-19T18:34:16.000Z",
  "updated": "2019-01-19T18:34:16.000Z",
  "title": "SIR epidemics on evolving graphs",
  "authors": [
    "Yufeng Jiang",
    "Remy Kassem",
    "Grayson York",
    "Matthew Junge",
    "Rick Durrett"
  ],
  "comment": "24 pages, 12 pictures",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider evoSIR, a variant of the SIR model, on Erd\\H os-Renyi random graphs in which susceptibles with an infected neighbor break that connection at rate $\\rho$ and rewire to a randomly chosen individual. We compute the critical infection rate $\\lambda_c$ and the probability of a large epidemic by showing that they are the same for the delSIR model in which $S-I$ connections are deleted instead of rewired. The final size of a large delSIR epidemic has a continuous transition. Simulations suggest that the final size of a large evoSIR epidemic is discontinuous at $\\lambda_c$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-19T18:34:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35"
    ],
    "keywords": [
      "sir epidemics",
      "evolving graphs",
      "large evosir epidemic",
      "os-renyi random graphs",
      "large delsir epidemic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 24,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}