Universality classes of the absorbing state transition in a system with interacting static and diffusive populations

Argolo, C.; Quintino, Yan; Siqueira, Y.; Gleria, Iram; Lyra, M. L.

doi:10.1103/physreve.80.061127

Cited by 12 publications

(9 citation statements)

References 19 publications

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“…The influence of particle diffusion in the critical behavior of absorbing state phase transitions has been a subject of growing interest, since analytical and numerical studies showed that diffusion is an important mechanism that can influence the critical behavior [5][6][7][8][9][10][11][12][13][14]. In particular, strong deviations from the directed percolation universality class have been recently reported for models with coupled diffusive and non-diffusive fields [15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

Argolo

Quintino

Gleria

et al. 2011

Physica A: Statistical Mechanics and its Applications

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a b s t r a c tWe investigate the critical behavior of a stochastic lattice model describing a General Epidemic Process. By means of a Monte Carlo procedure, we simulate the model on a regular square lattice and follow the spreading of an epidemic process with immunization. A finite size scaling analysis is employed to determine the critical point as well as some critical exponents. We show that the usual scaling analysis of the order parameter moment ratio does not provide an accurate estimate of the critical point. Precise estimates of the critical quantities are obtained from data of the order parameter variation rate and its fluctuations. Our numerical results corroborate that this model belongs to the dynamic isotropic percolation universality class. We also check the validity of the hyperscaling relation and present data collapse curves which reinforce the accuracy of the estimated critical parameters.

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Section: Introductionmentioning

confidence: 99%

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

Argolo

Quintino

Gleria

et al. 2011

Physica A: Statistical Mechanics and its Applications

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“…However, some progress was made (see, for example [2][3][4]). In order to model the spreading of a disease, we consider a metapopulation model [5] where we couple a population of random walkers to a network, called diffusive epidemic process (DEP) [6][7][8][9][10][11][12]. Unlike the common lattice epidemic models, where a sedentary individual is placed in a node, we consider a population of moving individuals that can hop along the network edges while they can be contaminated while dividing the same network node with an already contaminated individual.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we consider the DEP [6][7][8][9][10][11][12], coupled to BA networks. The DEP is a well-studied model where a non-sedentary population is divided into two compartments: susceptible individuals and infected individuals.…”

Section: Introductionmentioning

confidence: 99%

The diffusive epidemic process on Barabasi–Albert networks

Alves¹,

Alves²,

Filho³

et al. 2021

J. Stat. Mech.

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We present a modified diffusive epidemic process (DEP) that has a finite threshold on scale-free graphs, motivated by the COVID-19 pandemic. The DEP describes the epidemic spreading of a disease in a non-sedentary population, which can describe the spreading of a real disease. Our main modification is to use the Gillespie algorithm with a reaction time t max, exponentially distributed with mean inversely proportional to the node population in order to model the individuals’ interactions. Our simulation results of the modified model on Barabasi–Albert networks are compatible with a continuous absorbing-active phase transition when increasing the average concentration. The transition obeys the mean-field critical exponents β = 1, γ′ = 0 and ν ⊥ = 1/2. In addition, the system presents logarithmic corrections with pseudo-exponents β ̂ = γ ̂ ′ = − 3 / 2 on the order parameter and its fluctuations, respectively. The most evident implication of our simulation results is if the individuals avoid social interactions in order to not spread a disease, this leads the system to have a finite threshold in scale-free graphs.

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“…It is known that the models with local updates given by a contact process, when transport is dominated by brownian diffusion, can have different critical exponents in lower dimensions. The Diffusive Epidemic Process (DEP) [17][18][19][20][21][22][23][24][25][26] is an example of a system that presents a new universality class, where exponents in lower dimensions deviate from the exponents of the contact process (CP). The CP obeys the directed percolation (DP) universality class, and DEP in lower dimensions defines new universality classes [25].…”

Section: Introductionmentioning

confidence: 99%

Diffusive Majority Vote Model

Lima,

Alves

et al. 2021

Preprint

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We define a stochastic reaction-diffusion process that describes a consensus formation in a nonsedentary population. The process is a diffusive version of the Majority Vote model, where the state update follows two stages: in the first stage, spins are allowed to hop to neighbor nodes with different probabilities for the respective spin orientation, and in the second stage, the spins in the same node can change its values according to the majority vote update rule. The model presents a consensus formation phase when concentration is greater than a threshold value, and a paramagnetic phase on the converse for equal diffusion probabilities, i.e., maintaining the inversion symmetry. The threshold vanishes for unequal diffusion probabilities, which means that the system has a consensus state for all values of population densities. The stationary collective opinion is dominated by the individuals that diffuse more.

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Universality classes of the absorbing state transition in a system with interacting static and diffusive populations

Cited by 12 publications

References 19 publications

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

Finite-size scaling analysis of the critical behavior of a general epidemic process in 2D

The diffusive epidemic process on Barabasi–Albert networks

Diffusive Majority Vote Model

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