title: Long-range epidemic spreading in a random environment.
abstract: Modeling long-range epidemic spreading in a random environment, we consider a quenched, disordered, d-dimensional contact process with infection rates decaying with distance as 1/rd+σ. 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)∼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 zc=d+σ 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)∼t1/zc with a multiplicative logarithmic correction and the average number of infected sites in surviving trials is found to increase as Ns(t)∼(lnt)χ with χ=2 in one dimension.
authors: Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.
authors: Róbert
authors: R
authors: Juhász
authors: Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.|Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary.|Center for Complex Networks Research and Department of Physics, 111 Dana Research Center, Northeastern University, 110 Forsyth Street, Boston, Massachusetts 02115, USA.
authors: István A
authors: IA
authors: Kovács
authors: Wigner Research Centre for Physics, Institute for Solid State Physics and Optics, P.O. Box 49, H-1525 Budapest, Hungary.|Institute of Theoretical Physics, Szeged University, H-6720 Szeged, Hungary.
authors: Ferenc
authors: F
authors: Iglói
mesh_terms: D003141:Communicable Diseases / Q000453:epidemiology* / Q000635:transmission*; D058872:Epidemics; D008962:Models, Theoretical; D009010:Monte Carlo Method