Percolation and the pandemic

Ziff, Robert M.

doi:10.1016/j.physa.2020.125723

Cited by 43 publications

(35 citation statements)

References 48 publications

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“…Thus, we conclude that the site percolation threshold of the bcc-1,2 lattice to be p c = 0.1759432 (8), where the number in parentheses represents the estimated error in the last digit, by comprehensively considering the two methods mentioned above, as well as the errors for the values of τ , Ω and σ. The simulation results for the other three lattices we considered (bcc-1,2,3, fcc-1,2, and fcc-1,2,3) are shown in the Supplementary Material [67] in Figs.…”

Section: Iv1 Site Percolationmentioning

confidence: 92%

“…With regard to the universal exponents τ , Ω, and σ, in three dimensions, relatively accurate and acceptable results are known: 2.18906(8) [61], 2.18909(5) [62] for τ , 0.64(2) [60], 0.65(2) [63], 0.60 (8) [64], 0.64 (5) [65] for Ω, and 0.4522(8) [61], 0.45237(8) [62], 0.4419 [66] for σ. In our simulations, τ = 2.18905 (15), Ω = 0.63(4), and σ = 0.4522(2) are chosen.…”

Section: Site and Bond Percolation On Sc Bcc And Fcc Lattices With Ex...mentioning

confidence: 99%

“…In addition, bond percolation with extended neighbors is also similar to spatial models of the spread of epidemics via long-range links [28]. Just recently [8], it was pointed out how the threshold is related to the basic epidemic infectivity parameter R 0 , for trees (Bethe lattice), trees with triangular cliques, and non-planar lattices with extended-range connectivity.…”

Section: Introductionmentioning

confidence: 95%

“…It is well known that percolation is an important model in statistical physics [1,2]. As a paradigmatic model, it can describe diverse phenomena in various fields, such as liquids moving in porous media [3,4], forest-fire problems [5,6] and epidemics [7,8]. Considering percolation on a lattice, each edge (vertex) is occupied by a bond (site) with probability p, and clusters of neighboring occupied sites or connected bonds can be constructed.…”

Section: Introductionmentioning

confidence: 99%

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Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions

Xun,

Hao,

Ziff

2021

Preprint

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Extended-range percolation on various regular lattices, including all eleven Archimedean lattices in two dimensions, and the simple cubic (sc), body-centered cubic (bcc), and face-centered cubic (fcc) lattices in three dimensions, is investigated. In two dimensions, correlations between coordination number z and site thresholds pc for Archimedean lattices up to 10th nearest neighbors (NN) are seen by plotting z versus 1/pc and z versus −1/ ln(1 − pc), using the data of d'Iribarne et al. [J. Phys. A 32:2611[J. Phys. A 32: , 1999] and others. The results show that all the plots overlap on a line with a slope consistent with the theoretically predicted asymptotic value of zpc ∼ 4ηc = 4.51235, where ηc is the continuum threshold for disks. In three dimensions, precise site and bond thresholds for bcc and fcc lattices with 2nd and 3rd NN, and bond thresholds for the sc lattice with up to the 13th NN, are obtained by Monte-Carlo simulations, using an efficient single-cluster growth method. For site percolation, the values of thresholds for different types of lattices with compact neighborhoods also collapse together, and linear fitting is consistent with the predicted value of zpc ∼ 8ηc = 2.7351, where ηc is the continuum threshold for spheres. For bond percolation, Bethe-lattice behavior pc = 1/(z − 1) is expected to hold for large z, and the finite-z correction is confirmed to satisfy zpc − 1 ∼ a1z −x , with x = 2/3 for three dimensions as predicted by Frei and Perkins [Electron. J. Probab. 21:56, 2016] and by Xu et al. [Phys. Rev. E, 103:022127, 2021]. Our analysis indicates that for compact neighborhoods, the asymptotic behavior of zpc is universal, depending only upon the dimension of the system and whether site or bond percolation, but not upon the type of lattice.

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Section: Iv1 Site Percolationmentioning

confidence: 92%

Section: Site and Bond Percolation On Sc Bcc And Fcc Lattices With Ex...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions

Xun,

Hao,

Ziff

2021

Preprint

Self Cite

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“…e existence of the critical threshold p c makes percolation suitable to model numerous natural and engineering phenomena [11]. An oft-cited application is the modeling of liquid propagation in a porous medium, while a nowadays highly relevant application is the modeling of disease spread [12,13]. In the latter, the underlying graph is essentially a network of contacts where the adjacency of the sites defines the contacts.…”

Section: Introductionmentioning

confidence: 99%

A Size‐Perimeter Discrete Growth Model for Percolation Clusters

Bak

Kalmár‐Nagy

2021

Complexity

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Cluster growth models are utilized for a wide range of scientific and engineering applications, including modeling epidemics and the dynamics of liquid propagation in porous media. Invasion percolation is a stochastic branching process in which a network of sites is getting occupied that leads to the formation of clusters (group of interconnected, occupied sites). The occupation of sites is governed by their resistance distribution; the invasion annexes the sites with the least resistance. An iterative cluster growth model is considered for computing the expected size and perimeter of the growing cluster. A necessary ingredient of the model is the description of the mean perimeter as the function of the cluster size. We propose such a relationship for the site square lattice. The proposed model exhibits (by design) the expected phase transition of percolation models, i.e., it diverges at the percolation threshold p c . We describe an application for the porosimetry percolation model. The calculations of the cluster growth model compare well with simulation results.

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RETRACTED ARTICLE: Percolation Analysis of COVID-19 Epidemic

Kazemi,

Vahidi-Asl

2023

J Nonlinear Math Phys

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The spread of COVID-19 can be greatly influenced by human mobility. However, implementing control measures based on restrictions can be costly. That is why it is crucial to develop a quarantine strategy that can minimize the spread of the disease while also reducing costs. This article focuses on determining the percolation threshold of COVID-19 in Tehran province using a square lattice and two types of city connections. The study identifies the number of roads that need to be closed and the cities that should be quarantined. Monte Carlo simulations using the Newman and Ziff and Union-Find algorithms were conducted through the $$\text {SEAIRD}$$ SEAIRD model to assess the effectiveness of the proposed measures. The results showed a possible reduction of 81$$\%$$ % in disease spread. This approach can be used in other regions to assist in the development of public health policies.

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Percolation and the pandemic

Cited by 43 publications

References 48 publications

Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions

Universal behavior of site and bond percolation thresholds on regular lattices with compact extended-range neighborhoods in 2 and 3 dimensions

A Size‐Perimeter Discrete Growth Model for Percolation Clusters

RETRACTED ARTICLE: Percolation Analysis of COVID-19 Epidemic

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