Long-range epidemic spreading in a random environment

Juhász, Róbert and Kovács, István and Iglói, Ferenc (2015) Long-range epidemic spreading in a random environment. PHYSICAL REVIEW E - STATISTICAL, NONLINEAR AND SOFT MATTER PHYSICS (2001-2015), 91 (3). ISSN 1539-3755

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Abstract

Modeling long-range epidemic spreading in a random environment, we consider a quenched dis- ordered, d-dimensional contact process with infection rates decaying with the 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 multi- plicative logarithmic correction, and the average number of infected sites in surviving trials is found to increase as Ns(t) ∼ (ln t)χ with χ = 2 in one dimension.

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