{
  "id": "2002.02586",
  "version": "v1",
  "published": "2020-02-07T02:01:15.000Z",
  "updated": "2020-02-07T02:01:15.000Z",
  "title": "Traveling wave solutions for a class of discrete diffusive SIR epidemic model",
  "authors": [
    "Ran Zhang",
    "Jinliang Wang",
    "Shengqiang Liu"
  ],
  "categories": [
    "math.DS"
  ],
  "abstract": "This paper is concerned with the conditions of existence and nonexistence of traveling wave solutions (TWS) for a class of discrete diffusive epidemic models. We find that the existence of TWS is determined by the so-called basic reproduction number and the critical wave speed: When the basic reproduction number R0 greater than 1, there exists a critical wave speed c* > 0, such that for each c >= c * the system admits a nontrivial TWS and for c < c* there exists no nontrivial TWS for the system. In addition, the boundary asymptotic behaviour of TWS is obtained by constructing a suitable Lyapunov functional and employing Lebesgue dominated convergence theorem. Finally, we apply our results to two discrete diffusive epidemic models to verify the existence and nonexistence of TWS.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-02-07T02:01:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35C07",
      "35K57",
      "92D30"
    ],
    "keywords": [
      "discrete diffusive sir epidemic model",
      "traveling wave solutions",
      "reproduction number r0 greater",
      "lebesgue dominated convergence theorem",
      "discrete diffusive epidemic models"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}