Long-range epidemic spreading with immunization

Linder, Florian; Tran-Gia, Johannes; Dahmen, Sílvio R.; Hinrichsen, Haye

doi:10.1088/1751-8113/41/18/185005

Cited by 26 publications

(45 citation statements)

References 19 publications

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“…In between there is a region where the critical exponents depend on σ. Indeed, it is still an open question whether local OP behavior holds only down to σ = 2 or continues to hold down to σ ≈ 1.79 [65,66].…”

Section: Long Range Infectionsmentioning

confidence: 99%

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Phase transitions in cooperative coinfections: Simulation results for networks and lattices

et al. 2016

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We study the spreading of two mutually cooperative diseases on different network topologies, and with two microscopic realizations, both of which are stochastic versions of a susceptible-infected-removed type model studied by us recently in mean field approximation. There it had been found that cooperativity can lead to first order transitions from spreading to extinction. However, due to the rapid mixing implied by the mean field assumption, first order transitions required nonzero initial densities of sick individuals. For the stochastic model studied here the results depend strongly on the underlying network. First order transitions are found when there are few short but many long loops: (i) No first order transitions exist on trees and on 2-d lattices with local contacts. (ii) They do exist on Erdős-Rényi (ER) networks, on d-dimensional lattices with d≥4, and on 2-d lattices with sufficiently long-ranged contacts. (iii) On 3-d lattices with local contacts the results depend on the microscopic details of the implementation. (iv) While single infected seeds can always lead to infinite epidemics on regular lattices, on ER networks one sometimes needs finite initial densities of infected nodes. (v) In all cases the first order transitions are actually "hybrid"; i.e., they display also power law scaling usually associated with second order transitions. On regular lattices, our model can also be interpreted as the growth of an interface due to cooperative attachment of two species of particles. Critically pinned interfaces in this model seem to be in different universality classes than standard critically pinned interfaces in models with forbidden overhangs. Finally, the detailed results mentioned above hold only when both diseases propagate along the same network of links. If they use different links, results can be rather different in detail, but are similar overall.

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Section: Long Range Infectionsmentioning

confidence: 99%

“…In the following simulations we used the model without delay and the precise form of p(x) used in [65,66]. For each site we have three potential contacts distributed according to Eq.…”

Section: Long Range Infectionsmentioning

confidence: 99%

Phase transitions in cooperative coinfections: Simulation results for networks and lattices

et al. 2016

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“…Following Linder et al [8], we define p(x) for σ > 0 implicitly by the following simple algorithm: (i) We first chose two random numbers u, v uniformly from ]0, 1]×]0, 1]. (ii) If w 2 ≡ u 2 + v 2 >= 1, we discard them and choose a new pair until w 2 < 1.…”

Section: The Model and Basic Featuresmentioning

confidence: 99%

“…Critical exponents are mean field like for all σ < 2/3 (σ < d/3 for d spatial dimensions), i.e. to the left of point B [7,8]. For σ > 2/3 all critical exponents depend continuously on σ, until the short range regime is reached.…”

Section: The Model and Basic Featuresmentioning

confidence: 99%

Two-Dimensional SIR Epidemics with Long Range Infection

Grassberger

2013

J Stat Phys

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We extend a recent study of susceptible-infected-removed epidemic processes with long range infection (referred to as I in the following) from 1-dimensional lattices to lattices in two dimensions. As in I we use hashing to simulate very large lattices for which finite size effects can be neglected, in spite of the assumed power law p(x) ∼ |x| −σ−2 for the probability that a site can infect another site a distance vector x apart. As in I we present detailed results for the critical case, for the supercritical case with σ = 2, and for the supercritical case with 0 < σ < 2. For the latter we verify the stretched exponential growth of the infected cluster with time predicted by M. Biskup. For σ = 2 we find generic power laws with σ−dependent exponents in the supercritical phase, but no Kosterlitz-Thouless (KT) like critical point as in 1-d. Instead of diverging exponentially with the distance from the critical point, the correlation length increases with an inverse power, as in an ordinary critical point. Finally we study the dependence of the critical exponents on σ in the regime 0 < σ < 2, and compare with field theoretic predictions. In particular we discuss in detail whether the critical behavior for σ slightly less than 2 is in the short range universality class, as conjectured recently by F. Linder et al.. As in I we also consider a modified version of the model where only some of the contacts are long range, the others being between nearest neighbors. If the number of the latter reaches the percolation threshold, the critical behavior is changed but the supercritical behavior stays qualitatively the same.

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“…The main difference in critical behavior of this variant compared to that of the unrestricted one is the absence of a mean-field region. Long-range epidemic spreading has also been studied by other models, such as the susceptible-infected-recovered model [16,17]. For further studies in this field, we mention Refs.…”

Section: Introductionmentioning

confidence: 99%

Long-range epidemic spreading in a random environment

2015

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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+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) ∼ t 1/zc with a multiplicative 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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Long-range epidemic spreading with immunization

Cited by 26 publications

References 19 publications

Phase transitions in cooperative coinfections: Simulation results for networks and lattices

Phase transitions in cooperative coinfections: Simulation results for networks and lattices

Two-Dimensional SIR Epidemics with Long Range Infection

Long-range epidemic spreading in a random environment

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