{
  "id": "1411.3505",
  "version": "v1",
  "published": "2014-11-13T11:24:47.000Z",
  "updated": "2014-11-13T11:24:47.000Z",
  "title": "Long-range epidemic spreading in a random environment",
  "authors": [
    "R. Juhász",
    "I. A. Kovács",
    "F. Iglói"
  ],
  "comment": "12 pages, 6 figures",
  "categories": [
    "cond-mat.dis-nn",
    "cond-mat.stat-mech",
    "q-bio.PE"
  ],
  "abstract": "Modeling long-range epidemic spreading in a random environment, we consider a quenched disordered, $d$-dimensional contact process with infection rates decaying with the distance as $1/r^{d+\\sigma}$. We study the dynamical behavior of the model at and below the epidemic threshold by a variant of the strong-disorder renormalization group method and by Monte Carlo simulations in one and two spatial dimensions. Starting from a single infected site, the average survival probability is found to decay as $P(t) \\sim t^{-d/z}$ up to multiplicative logarithmic corrections. Below the epidemic threshold, a Griffiths phase emerges, where the dynamical exponent $z$ varies continuously with the control parameter and tends to $z_c=d+\\sigma$ as the threshold is approached. At the threshold, the spatial extension of the infected cluster (in surviving trials) is found to grow as $R(t) \\sim t^{1/z_c}$ with a multiplicative logarithmic correction, and the average number of infected sites in surviving trials is found to increase as $N_s(t) \\sim (\\ln t)^{\\chi}$ with $\\chi=2$ in one dimension.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-13T11:24:47.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05.70.Ln",
      "64.60.ae",
      "87.23.Cc"
    ],
    "keywords": [
      "long-range epidemic spreading",
      "random environment",
      "multiplicative logarithmic correction",
      "epidemic threshold",
      "strong-disorder renormalization group method"
    ],
    "publication": {
      "doi": "10.1103/PhysRevE.91.032815",
      "journal": "Physical Review E",
      "year": 2015,
      "month": "Mar",
      "volume": 91,
      "number": 3,
      "pages": "032815"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015PhRvE..91c2815J"
    }
  }
}