### 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 language | English |
---|---|

Article number | 032815 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 91 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 31 2015 |

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### ASJC Scopus subject areas

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

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*91*(3), [032815]. https://doi.org/10.1103/PhysRevE.91.032815

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

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 91, no. 3, 032815. https://doi.org/10.1103/PhysRevE.91.032815

}

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 -