Long-range epidemic spreading in a random environment

Róbert Juhász, István A. Kovács, F. Iglói

Research output: Contribution to journalArticle

8 Citations (Scopus)

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.

Original languageEnglish
Article number032815
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume91
Issue number3
DOIs
Publication statusPublished - Mar 31 2015

Fingerprint

Epidemic Spreading
Random Environment
thresholds
Range of data
Multiplicative
Logarithmic
Contact Process
Survival Probability
renormalization group methods
infectious diseases
Dynamical Behavior
Renormalization Group
Control Parameter
One Dimension
Infection
Disorder
Monte Carlo Simulation
Exponent
Vary
exponents

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Long-range epidemic spreading in a random environment. / Juhász, Róbert; Kovács, István A.; Iglói, F.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 91, No. 3, 032815, 31.03.2015.

Research output: Contribution to journalArticle

@article{6b6391b6c4ae49089eb6fb8b54b84ee5,
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.",
author = "R{\'o}bert Juh{\'a}sz and Kov{\'a}cs, {Istv{\'a}n A.} and F. Igl{\'o}i",
year = "2015",
month = "3",
day = "31",
doi = "10.1103/PhysRevE.91.032815",
language = "English",
volume = "91",
journal = "Physical review. E",
issn = "2470-0045",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Long-range epidemic spreading in a random environment

AU - Juhász, Róbert

AU - Kovács, István A.

AU - Iglói, F.

PY - 2015/3/31

Y1 - 2015/3/31

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84928778135&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84928778135&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.91.032815

DO - 10.1103/PhysRevE.91.032815

M3 - Article

C2 - 25871165

AN - SCOPUS:84928778135

VL - 91

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 3

M1 - 032815

ER -