1
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Gascuel HM, Rahmani P, Bon R, Peruani F. Generic Coupling between Internal States and Activity Leads to Activation Fronts and Criticality in Active Systems. PHYSICAL REVIEW LETTERS 2024; 133:058301. [PMID: 39159097 DOI: 10.1103/physrevlett.133.058301] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/21/2023] [Revised: 04/24/2024] [Accepted: 06/05/2024] [Indexed: 08/21/2024]
Abstract
To understand the onset of collective motion, we investigate active systems where particles switch on and off their self-propulsion. We prove that even when the only possible transition is off→on, an active two-state system behaves as an effective three-state (inactive/passive) system that exhibits a sharp phase transition in 1D, and critical behavior in 2D, with scale-invariant activity avalanches. The obtained results show how criticality can naturally emerge in active systems, providing insight into the way collectives distribute, process, and respond to local environmental cues.
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2
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Moraes JT, Ferreira SC. Visibility graphs of critical and off-critical time series for absorbing state phase transitions. Phys Rev E 2023; 108:044309. [PMID: 37978633 DOI: 10.1103/physreve.108.044309] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/19/2023] [Accepted: 09/11/2023] [Indexed: 11/19/2023]
Abstract
It is possible to investigate emergence in many real systems using time-ordered data. However, classical time series analysis is usually conditioned by data accuracy and quantity. A modern method is to map time series onto graphs and study these structures using the toolbox available in complex network analysis. An important practical problem to investigate the criticality in experimental systems is to determine whether an observed time series is associated with a critical regime or not. We contribute to this problem by investigating the mapping called visibility graph (VG) of a time series generated in dynamical processes with absorbing-state phase transitions. Analyzing degree correlation patterns of the VGs, we are able to distinguish between critical and off-critical regimes. One central hallmark is an asymptotic disassortative correlation on the degree for series near the critical regime in contrast with a pure assortative correlation observed for noncritical dynamics. We are also able to distinguish between continuous (critical) and discontinuous (noncritical) absorbing state phase transitions, the second of which is commonly involved in catastrophic phenomena. The determination of critical behavior converges very quickly in higher dimensions, where many complex system dynamics are relevant.
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Affiliation(s)
- Juliane T Moraes
- Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
| | - Silvio C Ferreira
- Departamento de Física, Universidade Federal de Viçosa, 36570-900 Viçosa, Minas Gerais, Brazil
- National Institute of Science and Technology for Complex Systems, 22290-180, Rio de Janeiro, Brazil
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3
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Feshanjerdi M, Masoudi AA, Grassberger P, Ebrahimi M. Aftermath epidemics: Percolation on the sites visited by generalized random walks. Phys Rev E 2023; 108:024312. [PMID: 37723758 DOI: 10.1103/physreve.108.024312] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/14/2023] [Accepted: 07/21/2023] [Indexed: 09/20/2023]
Abstract
We study percolation on the sites of a finite lattice visited by a generalized random walk of finite length with periodic boundary conditions. More precisely, consider Levy flights and walks with finite jumps of length >1 [like Knight's move random walks (RWs) in two dimensions and generalized Knight's move RWs in 3D]. In these walks, the visited sites do not form (as in ordinary RWs) a single connected cluster, and thus percolation on them is nontrivial. The model essentially mimics the spreading of an epidemic in a population weakened by the passage of some devastating agent-like diseases in the wake of a passing army or of a hurricane. Using the density of visited sites (or the number of steps in the walk) as a control parameter, we find a true continuous percolation transition in all cases except for the 2D Knight's move RWs and Levy flights with Levy parameter σ≥2. For 3D generalized Knight's move RWs, the model is in the universality class of pacman percolation, and all critical exponents seem to be simple rationals, in particular, β=1. For 2D Levy flights with 0<σ<2, scale invariance is broken even at the critical point, which leads at least to very large corrections in finite-size scaling, and even very large simulations were unable to unambiguously determine the critical exponents.
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Affiliation(s)
- Mohadeseh Feshanjerdi
- Department of Condensed Matter Physics, Faculty of Physics, Alzahra University, P.O. Box 1993893973, Tehran, Iran
| | - Amir Ali Masoudi
- Department of Condensed Matter Physics, Faculty of Physics, Alzahra University, P.O. Box 1993893973, Tehran, Iran
| | | | - Mahdieh Ebrahimi
- Institute of Condensed Matter Physics, Technical University of Darmstadt, Hochschulstr. 6, 64289 Darmstadt, Germany
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4
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Merbis W, de Mulatier C, Corboz P. Efficient simulations of epidemic models with tensor networks: Application to the one-dimensional susceptible-infected-susceptible model. Phys Rev E 2023; 108:024303. [PMID: 37723790 DOI: 10.1103/physreve.108.024303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Accepted: 07/20/2023] [Indexed: 09/20/2023]
Abstract
The contact process is an emblematic model of a nonequilibrium system, containing a phase transition between inactive and active dynamical regimes. In the epidemiological context, the model is known as the susceptible-infected-susceptible model, and it is widely used to describe contagious spreading. In this work, we demonstrate how accurate and efficient representations of the full probability distribution over all configurations of the contact process on a one-dimensional chain can be obtained by means of matrix product states (MPSs). We modify and adapt MPS methods from many-body quantum systems to study the classical distributions of the driven contact process at late times. We give accurate and efficient results for the distribution of large gaps, and illustrate the advantage of our methods over Monte Carlo simulations. Furthermore, we study the large deviation statistics of the dynamical activity, defined as the total number of configuration changes along a trajectory, and investigate quantum-inspired entropic measures, based on the second Rényi entropy.
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Affiliation(s)
- Wout Merbis
- Dutch Institute for Emergent Phenomena (DIEP) & Institute for Theoretical Physics (ITFA), University of Amsterdam, 1090 GL Amsterdam, The Netherlands
| | - Clélia de Mulatier
- Dutch Institute for Emergent Phenomena (DIEP) & Institute for Theoretical Physics (ITFA), University of Amsterdam, 1090 GL Amsterdam, The Netherlands
| | - Philippe Corboz
- Dutch Institute for Emergent Phenomena (DIEP) & Institute for Theoretical Physics (ITFA), University of Amsterdam, 1090 GL Amsterdam, The Netherlands
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5
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Brabers JHVJ. The spread of infectious diseases from a physics perspective. Biol Methods Protoc 2023; 8:bpad010. [PMID: 37662617 PMCID: PMC10469146 DOI: 10.1093/biomethods/bpad010] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/17/2022] [Revised: 05/23/2023] [Accepted: 05/25/2023] [Indexed: 09/05/2023] Open
Abstract
This article deals with the spread of infectious diseases from a physics perspective. It considers a population as a network of nodes representing the population members, linked by network edges representing the (social) contacts of the individual population members. Infections spread along these edges from one node (member) to another. This article presents a novel, modified version of the SIR compartmental model, able to account for typical network effects and percolation phenomena. The model is successfully tested against the results of simulations based on Monte-Carlo methods. Expressions for the (basic) reproduction numbers in terms of the model parameters are presented, and justify some mild criticisms on the widely spread interpretation of reproduction numbers as being the number of secondary infections due to a single active infection. Throughout the article, special emphasis is laid on understanding, and on the interpretation of phenomena in terms of concepts borrowed from condensed-matter and statistical physics, which reveals some interesting analogies. Percolation effects are of particular interest in this respect and they are the subject of a detailed investigation. The concept of herd immunity (its definition and nature) is intensively dealt with as well, also in the context of large-scale vaccination campaigns and waning immunity. This article elucidates how the onset of herd-immunity can be considered as a second-order phase transition in which percolation effects play a crucial role, thus corroborating, in a more pictorial/intuitive way, earlier viewpoints on this matter. An exact criterium for the most relevant form of herd-immunity to occur can be derived in terms of the model parameters. The analyses presented in this article provide insight in how various measures to prevent an epidemic spread of an infection work, how they can be optimized and what potentially deceptive issues have to be considered when such measures are either implemented or scaled down.
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6
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Valdez LD, Vassallo L, Braunstein LA. Epidemic control in networks with cliques. Phys Rev E 2023; 107:054304. [PMID: 37329038 DOI: 10.1103/physreve.107.054304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/26/2022] [Accepted: 04/13/2023] [Indexed: 06/18/2023]
Abstract
Social units, such as households and schools, can play an important role in controlling epidemic outbreaks. In this work, we study an epidemic model with a prompt quarantine measure on networks with cliques (a clique is a fully connected subgraph representing a social unit). According to this strategy, newly infected individuals are detected and quarantined (along with their close contacts) with probability f. Numerical simulations reveal that epidemic outbreaks in networks with cliques are abruptly suppressed at a transition point f_{c}. However, small outbreaks show features of a second-order phase transition around f_{c}. Therefore, our model can exhibit properties of both discontinuous and continuous phase transitions. Next, we show analytically that the probability of small outbreaks goes continuously to 1 at f_{c} in the thermodynamic limit. Finally, we find that our model exhibits a backward bifurcation phenomenon.
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Affiliation(s)
- L D Valdez
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata-CONICET, Mar del Plata 7600, Argentina
| | - L Vassallo
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata-CONICET, Mar del Plata 7600, Argentina
| | - L A Braunstein
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata-CONICET, Mar del Plata 7600, Argentina
- Physics Department, Boston University, Boston, Massachusetts 02215, USA
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7
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Patwardhan S, Radicchi F, Fortunato S. Influence maximization: Divide and conquer. Phys Rev E 2023; 107:054306. [PMID: 37329077 DOI: 10.1103/physreve.107.054306] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/03/2022] [Accepted: 05/03/2023] [Indexed: 06/18/2023]
Abstract
The problem of influence maximization, i.e., finding the set of nodes having maximal influence on a network, is of great importance for several applications. In the past two decades, many heuristic metrics to spot influencers have been proposed. Here, we introduce a framework to boost the performance of such metrics. The framework consists in dividing the network into sectors of influence, and then selecting the most influential nodes within these sectors. We explore three different methodologies to find sectors in a network: graph partitioning, graph hyperbolic embedding, and community structure. The framework is validated with a systematic analysis of real and synthetic networks. We show that the gain in performance generated by dividing a network into sectors before selecting the influential spreaders increases as the modularity and heterogeneity of the network increase. Also, we show that the division of the network into sectors can be efficiently performed in a time that scales linearly with the network size, thus making the framework applicable to large-scale influence maximization problems.
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Affiliation(s)
- Siddharth Patwardhan
- Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - Filippo Radicchi
- Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - Santo Fortunato
- Center for Complex Networks and Systems Research, Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
- Indiana University Network Science Institute (IUNI), Indiana Univeristy, Bloomington, Indiana 47408, USA
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8
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Libál A, Forgács P, Néda Á, Reichhardt C, Hengartner N, Reichhardt CJO. Transition from susceptible-infected to susceptible-infected-recovered dynamics in a susceptible-cleric-zombie-recovered active matter model. Phys Rev E 2023; 107:024604. [PMID: 36932562 DOI: 10.1103/physreve.107.024604] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/13/2022] [Accepted: 12/18/2022] [Indexed: 06/18/2023]
Abstract
The susceptible-infected (SI) and susceptible-infected-recovered (SIR) models provide two distinct representations of epidemic evolution, distinguished by whether or not the number of susceptibles always drops to zero at long times. Here we introduce a new active matter epidemic model, the "susceptible-cleric-zombie-recovered" (SCZR) model, in which spontaneous recovery is absent but zombies can recover with probability γ via interaction with a cleric. Upon colliding with a zombie, both susceptibles and clerics enter the zombie state with probability β and α, respectively. By changing the initial fraction of clerics or their healing ability rate γ, we can tune the SCZR model between SI dynamics, in which no susceptibles or clerics remain at long times, and SIR dynamics, in which a finite number of clerics and susceptibles survive at long times. The model is relevant to certain real world diseases such as HIV where spontaneous recovery is impossible but where medical interventions by a limited number of caregivers can reduce or eliminate the spread of infection.
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Affiliation(s)
- A Libál
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
| | - P Forgács
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
| | - Á Néda
- Mathematics and Computer Science Department, Babeş-Bolyai University, Cluj-Napoca 400084, Romania
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - N Hengartner
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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9
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Sommers GM, Gullans MJ, Huse DA. Self-dual quasiperiodic percolation. Phys Rev E 2023; 107:024137. [PMID: 36932570 DOI: 10.1103/physreve.107.024137] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2022] [Accepted: 01/20/2023] [Indexed: 06/18/2023]
Abstract
How does the percolation transition behave in the absence of quenched randomness? To address this question, we study two nonrandom self-dual quasiperiodic models of square-lattice bond percolation. In both models, the critical point has emergent discrete scale invariance, but none of the additional emergent conformal symmetry of critical random percolation. From the discrete sequences of critical clusters, we find fractal dimensions of D_{f}=1.911943(1) and D_{f}=1.707234(40) for the two models, significantly different from D_{f}=91/48=1.89583... of random percolation. The critical exponents ν, determined through a numerical study of cluster sizes and wrapping probabilities on a torus, are also well below the ν=4/3 of random percolation. While these new models do not appear to belong to a universality class, they demonstrate how the removal of randomness can fundamentally change the critical behavior.
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Affiliation(s)
- Grace M Sommers
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
| | - Michael J Gullans
- Joint Center for Quantum Information and Computer Science, NIST/University of Maryland, College Park, Maryland 20742, USA
| | - David A Huse
- Department of Physics, Princeton University, Princeton, New Jersey 08544, USA
- Institute for Advanced Study, Princeton, New Jersey 08540, USA
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10
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Abstract
In this article, we develop two independent and new approaches to model epidemic spread in a network. Contrary to the most studied models, those developed here allow for contacts with different probabilities of transmitting the disease (transmissibilities). We then examine each of these models using some mean field type approximations. The first model looks at the late-stage effects of an epidemic outbreak and allows for the computation of the probability that a given vertex was infected. This computation is based on a mean field approximation and only depends on the number of contacts and their transmissibilities. This approach shares many similarities with percolation models in networks. The second model we develop is a dynamic model which we analyze using a mean field approximation which highly reduces the dimensionality of the system. In particular, the original system which individually analyses each vertex of the network is reduced to one with as many equations as different transmissibilities. Perhaps the greatest contribution of this article is the observation that, in both these models, the existence and size of an epidemic outbreak are linked to the properties of a matrix which we call the [Formula: see text]-matrix. This is a generalization of the basic reproduction number which more precisely characterizes the main routes of infection.
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11
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Deng S, Ódor G. Critical behavior of the diffusive susceptible-infected-recovered model. Phys Rev E 2023; 107:014303. [PMID: 36797889 DOI: 10.1103/physreve.107.014303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/26/2022] [Accepted: 01/04/2023] [Indexed: 06/18/2023]
Abstract
The critical behavior of the nondiffusive susceptible-infected-recovered model on lattices had been well established in virtue of its duality symmetry. By performing simulations and scaling analyses for the diffusive variant on the two-dimensional lattice, we show that diffusion for all agents, while rendering this symmetry destroyed, constitutes a singular perturbation that induces asymptotically distinct dynamical and stationary critical behavior from the nondiffusive model. In particular, the manifested crossover behavior in the effective mean-square radius exponents reveals that slow crossover behavior in general diffusive multispecies reaction systems may be ascribed to the interference of multiple length scales and timescales at early times.
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Affiliation(s)
- Shengfeng Deng
- Institute of Technical Physics and Materials Science, Centre for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary
| | - Géza Ódor
- Institute of Technical Physics and Materials Science, Centre for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary
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12
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Sontag A, Rogers T, Yates CA. Stochastic drift in discrete waves of nonlocally interacting particles. Phys Rev E 2023; 107:014128. [PMID: 36797943 DOI: 10.1103/physreve.107.014128] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Accepted: 12/09/2022] [Indexed: 06/18/2023]
Abstract
In this paper, we investigate a generalized model of N particles undergoing second-order nonlocal interactions on a lattice. Our results have applications across many research areas, including the modeling of migration, information dynamics, and Muller's ratchet-the irreversible accumulation of deleterious mutations in an evolving population. Strikingly, numerical simulations of the model are observed to deviate significantly from its mean-field approximation even for large population sizes. We show that the disagreement between deterministic and stochastic solutions stems from finite-size effects that change the propagation speed and cause the position of the wave to fluctuate. These effects are shown to decay anomalously as (lnN)^{-2} and (lnN)^{-3}, respectively-much slower than the usual N^{-1/2} factor. Our results suggest that the accumulation of deleterious mutations in a Muller's ratchet and the loss of awareness in a population may occur much faster than predicted by the corresponding deterministic models. The general applicability of our model suggests that this unexpected scaling could be important in a wide range of real-world applications.
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Affiliation(s)
- Andrei Sontag
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
| | - Tim Rogers
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
| | - Christian A Yates
- Centre for Mathematical Biology, Department of Mathematical Sciences, University of Bath, Bath, BA2 7AY, United Kingdom
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13
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Galvani A, Trombettoni A, Gori G. High-precision anomalous dimension of three-dimensional percolation and spatial profile of the critical giant cluster. Phys Rev E 2022; 106:064111. [PMID: 36671093 DOI: 10.1103/physreve.106.064111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2021] [Accepted: 11/14/2022] [Indexed: 06/17/2023]
Abstract
In three-dimensional percolation, we apply and test the critical geometry approach for bounded critical phenomena based on the fractional Yamabe equation. The method predicts the functional shape of the order parameter profile ϕ, which is obtained by raising the solution of the Yamabe equation to the scaling dimension Δ_{ϕ}. The latter can be fixed from outcomes of numerical simulations, from which we obtain Δ_{ϕ}=0.47846(71) and the corresponding value of the anomalous dimension η=-0.0431(14). The comparison with values of η determined by using scaling relations is discussed. A test of hyperscaling is also performed.
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Affiliation(s)
- Alessandro Galvani
- SISSA and INFN, Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy
| | - Andrea Trombettoni
- SISSA and INFN, Sezione di Trieste, Via Bonomea 265, I-34136 Trieste, Italy
- Department of Physics, University of Trieste, Strada Costiera 11, I-34151 Trieste, Italy
| | - Giacomo Gori
- Institut für Theoretische Physik, Universität Heidelberg, D-69120 Heidelberg, Germany
- CNR-IOM DEMOCRITOS Simulation Center and SISSA, Via Bonomea 265, I-34136 Trieste, Italy
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14
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Chulahwat A, Mahmoud H, Monedero S, Diez Vizcaíno FJ, Ramirez J, Buckley D, Forradellas AC. Integrated graph measures reveal survival likelihood for buildings in wildfire events. Sci Rep 2022; 12:15954. [PMID: 36153344 PMCID: PMC9509321 DOI: 10.1038/s41598-022-19875-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2022] [Accepted: 09/06/2022] [Indexed: 11/09/2022] Open
Abstract
Wildfire events have resulted in unprecedented social and economic losses worldwide in the last few years. Most studies on reducing wildfire risk to communities focused on modeling wildfire behavior in the wildland to aid in developing fuel reduction and fire suppression strategies. However, minimizing losses in communities and managing risk requires a holistic approach to understanding wildfire behavior that fully integrates the wildland's characteristics and the built environment's features. This complete integration is particularly critical for intermixed communities where the wildland and the built environment coalesce. Community-level wildfire behavior that captures the interaction between the wildland and the built environment, which is necessary for predicting structural damage, has not received sufficient attention. Predicting damage to the built environment is essential in understanding and developing fire mitigation strategies to make communities more resilient to wildfire events. In this study, we use integrated concepts from graph theory to establish a relative vulnerability metric capable of quantifying the survival likelihood of individual buildings within a wildfire-affected region. We test the framework by emulating the damage observed in the historic 2018 Camp Fire and the 2020 Glass Fire. We propose two formulations based on graph centralities to evaluate the vulnerability of buildings relative to each other. We then utilize the relative vulnerability values to determine the damage state of individual buildings. Based on a one-to-one comparison of the calculated and observed damages, the maximum predicted building survival accuracy for the two formulations ranged from [Formula: see text] for the historical wildfires tested. From the results, we observe that the modified random walk formulation can better identify nodes that lie at the extremes on the vulnerability scale. In contrast, the modified degree formulation provides better predictions for nodes with mid-range vulnerability values.
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Affiliation(s)
- Akshat Chulahwat
- Department of Civil and Environmental Engineering, Colorado State University, Colorado, CO, 80523, USA
| | - Hussam Mahmoud
- Department of Civil and Environmental Engineering, Colorado State University, Colorado, CO, 80523, USA.
| | | | | | - Joaquin Ramirez
- Technosylva Inc., La Jolla, CA, USA
- Universidad de León, León, Spain
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15
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Mukhamadiarov RI, Täuber UC. Effects of lattice dilution on the nonequilibrium phase transition in the stochastic susceptible-infectious-recovered model. Phys Rev E 2022; 106:034132. [PMID: 36266833 DOI: 10.1103/physreve.106.034132] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/09/2022] [Accepted: 09/09/2022] [Indexed: 06/16/2023]
Abstract
We investigate how site dilution, as would be introduced by immunization, affects the properties of the active-to-absorbing nonequilibrium phase transition in the paradigmatic susceptible-infectious-recovered (SIR) model on regular cubic lattices. According to the Harris criterion, the critical behavior of the SIR model, which is governed by the universal scaling exponents of the dynamic isotropic percolation (DyIP) universality class, should remain unaltered after introducing impurities. However, when the SIR reactions are simulated for immobile agents on two- and three-dimensional lattices subject to quenched disorder, we observe a wide crossover region characterized by varying effective exponents. Only after a sufficient increase of the lattice sizes does it become clear that the SIR system must transition from that crossover regime before the effective critical exponents asymptotically assume the expected DyIP values. We attribute the appearance of this exceedingly long crossover to a time lag in a complete recovery of small disconnected clusters of susceptible sites, which are apt to be generated when the system is prepared with Poisson-distributed quenched disorder. Finally, we demonstrate that this transient region becomes drastically diminished when we significantly increase the value of the recovery rate or enable diffusive agent mobility through short-range hopping.
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Affiliation(s)
- Ruslan I Mukhamadiarov
- Max Planck Institute for the Physics of Complex Systems, Nöthnitzer Strasse 38, Dresden, D-01138, Germany
| | - Uwe C Täuber
- Department of Physics & Center for Soft Matter and Biological Physics (MC 0435), Robeson Hall, 850 West Campus Drive, Virginia Tech, Blacksburg, Virginia 24061, USA
- Faculty of Health Sciences, Virginia Tech, Blacksburg, Virginia 24061, USA
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16
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Mitra S, Saha D, Sensharma A. Percolation in a simple cubic lattice with distortion. Phys Rev E 2022; 106:034109. [PMID: 36266842 DOI: 10.1103/physreve.106.034109] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/08/2022] [Accepted: 08/22/2022] [Indexed: 06/16/2023]
Abstract
Site percolation in a distorted simple cubic lattice is characterized numerically employing the Newman-Ziff algorithm. Distortion is administered in the lattice by systematically and randomly dislocating its sites from their regular positions. The amount of distortion is tunable by a parameter called the distortion parameter. In this model, two occupied neighboring sites are considered connected only if the distance between them is less than a predefined value called the connection threshold. It is observed that the percolation threshold always increases with distortion if the connection threshold is equal to or greater than the lattice constant of the regular lattice. On the other hand, if the connection threshold is less than the lattice constant, the percolation threshold first decreases and then increases steadily as distortion is increased. It is shown that the variation of the percolation threshold can be well explained by the change in the fraction of occupied bonds with distortion. The values of the relevant critical exponents of the transition strongly indicate that percolation in regular and distorted simple cubic lattices belong to the same universality class. It is also demonstrated that this model is intrinsically distinct from the site-bond percolation model.
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Affiliation(s)
- Sayantan Mitra
- Department of Physics, University of Gour Banga, Malda - 732103, West Bengal, India
| | - Dipa Saha
- Department of Physics, University of Gour Banga, Malda - 732103, West Bengal, India
| | - Ankur Sensharma
- Department of Physics, University of Gour Banga, Malda - 732103, West Bengal, India
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17
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Machado G, Baxter GJ. Effect of initial infection size on a network susceptible-infected-recovered model. Phys Rev E 2022; 106:014307. [PMID: 35974578 DOI: 10.1103/physreve.106.014307] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2022] [Accepted: 06/30/2022] [Indexed: 06/15/2023]
Abstract
We consider the effect of a nonvanishing fraction of initially infected nodes (seeds) on the susceptible-infected-recovered epidemic model on random networks. This is relevant when the number of arriving infected individuals is large, or to the spread of ideas with publicity campaigns. This model is frequently studied by mapping to a bond percolation problem, in which edges are occupied with the probability p of eventual infection along an edge. This gives accurate measures of the final size of the infection and epidemic threshold in the limit of a vanishingly small seed fraction. We show, however, that when the initial infection occupies a nonvanishing fraction, f, of the network, this method yields ambiguous results, as the correspondence between edge occupation and contagion transmission no longer holds. We propose instead to measure the giant component of recovered individuals within the original contact network. We derive exact equations for the size of the epidemic and the epidemic threshold in the infinite size limit in heterogeneous sparse random networks, and we confirm them with numerical results. We observe that the epidemic threshold correctly depends on f, decreasing as f increases. When the seed fraction tends to zero, we recover the standard results.
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Affiliation(s)
- G Machado
- Department of Physics & I3N, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
| | - G J Baxter
- Department of Physics & I3N, University of Aveiro, Campus Universitário de Santiago, 3810-193 Aveiro, Portugal
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18
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Denk J, Hallatschek O. Self-consistent dispersal puts tight constraints on the spatiotemporal organization of species-rich metacommunities. Proc Natl Acad Sci U S A 2022; 119:e2200390119. [PMID: 35727977 PMCID: PMC9245702 DOI: 10.1073/pnas.2200390119] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/19/2022] [Accepted: 04/19/2022] [Indexed: 11/21/2022] Open
Abstract
Biodiversity is often attributed to a dynamic equilibrium between the immigration and extinction of species. This equilibrium forms a common basis for studying ecosystem assembly from a static reservoir of migrants-the mainland. Yet, natural ecosystems often consist of many coupled communities (i.e., metacommunities), and migration occurs between these communities. The pool of migrants then depends on what is sustained in the ecosystem, which, in turn, depends on the dynamic migrant pool. This chicken-and-egg problem of survival and dispersal is poorly understood in communities of many competing species, except for the neutral case-the "unified neutral theory of biodiversity." Employing spatiotemporal simulations and mean-field analyses, we show that self-consistent dispersal puts rather tight constraints on the dynamic migration-extinction equilibrium. When the number of species is large, species are pushed to the edge of their global extinction, even when competition is weak. As a consequence, the overall diversity is highly sensitive to perturbations in demographic parameters, including growth and dispersal rates. When dispersal is short range, the resulting spatiotemporal abundance patterns follow broad scale-free distributions that correspond to a directed percolation phase transition. The qualitative agreement of our results for short-range and long-range dispersal suggests that this self-organization process is a general property of species-rich metacommunities. Our study shows that self-sustaining metacommunities are highly sensitive to environmental change and provides insights into how biodiversity can be rescued and maintained.
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Affiliation(s)
- Jonas Denk
- Department of Physics, University of California, Berkeley, CA 94720
- Department of Integrative Biology, University of California, Berkeley, CA 94720
| | - Oskar Hallatschek
- Department of Physics, University of California, Berkeley, CA 94720
- Department of Integrative Biology, University of California, Berkeley, CA 94720
- Peter Debye Institute for Soft Matter Physics, Leipzig University, 04103 Leipzig, Germany
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19
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Cacciapaglia G, Cot C, de Hoffer A, Hohenegger S, Sannino F, Vatani S. Epidemiological theory of virus variants. PHYSICA A 2022; 596:127071. [PMID: 35185268 PMCID: PMC8848575 DOI: 10.1016/j.physa.2022.127071] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/08/2021] [Revised: 12/15/2021] [Indexed: 05/02/2023]
Abstract
We propose a physics-inspired mathematical model underlying the temporal evolution of competing virus variants that relies on the existence of (quasi) fixed points capturing the large time scale invariance of the dynamics. To motivate our result we first modify the time-honoured compartmental models of the SIR type to account for the existence of competing variants and then show how their evolution can be naturally re-phrased in terms of flow equations ending at quasi fixed points. As the natural next step we employ (near) scale invariance to organise the time evolution of the competing variants within the effective description of the epidemic Renormalisation Group framework. We test the resulting theory against the time evolution of COVID-19 virus variants that validate the theory empirically.
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Affiliation(s)
- Giacomo Cacciapaglia
- Institut de Physique des 2 Infinis (IP2I) de Lyon, CNRS/IN2P3, UMR5822, 69622 Villeurbanne, France
- Université de Lyon, Université Claude Bernard Lyon 1, 69001 Lyon, France
| | - Corentin Cot
- Institut de Physique des 2 Infinis (IP2I) de Lyon, CNRS/IN2P3, UMR5822, 69622 Villeurbanne, France
- Université de Lyon, Université Claude Bernard Lyon 1, 69001 Lyon, France
| | | | - Stefan Hohenegger
- Institut de Physique des 2 Infinis (IP2I) de Lyon, CNRS/IN2P3, UMR5822, 69622 Villeurbanne, France
- Université de Lyon, Université Claude Bernard Lyon 1, 69001 Lyon, France
| | - Francesco Sannino
- Scuola Superiore Meridionale, Largo S. Marcellino, 10, 80138 Napoli NA, Italy
- Dipartimento di Fisica, E. Pancini, Univ. di Napoli, Federico II and INFN sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, 80126 Napoli, Italy
- CP-Origins and D-IAS, Univ. of Southern Denmark, Campusvej 55, DK-5230 Odense, Denmark
| | - Shahram Vatani
- Institut de Physique des 2 Infinis (IP2I) de Lyon, CNRS/IN2P3, UMR5822, 69622 Villeurbanne, France
- Université de Lyon, Université Claude Bernard Lyon 1, 69001 Lyon, France
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20
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From subcritical behavior to a correlation-induced transition in rumor models. Nat Commun 2022; 13:3049. [PMID: 35650264 PMCID: PMC9160067 DOI: 10.1038/s41467-022-30683-z] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2021] [Accepted: 05/11/2022] [Indexed: 11/24/2022] Open
Abstract
Rumors and information spreading emerge naturally from human-to-human interactions and have a growing impact on our everyday life due to increasing and faster access to information, whether trustworthy or not. A popular mathematical model for spreading rumors, data, or news is the Maki–Thompson model. Mean-field approximations suggested that this model does not have a phase transition, with rumors always reaching a fraction of the population. Conversely, here, we show that a continuous phase transition is present in this model. Moreover, we explore a modified version of the Maki–Thompson model that includes a forgetting mechanism, changing the Markov chain’s nature and allowing us to use a plethora of analytic and numeric methods. Particularly, we characterize the subcritical behavior, where the lifespan of a rumor increases as the spreading rate drops, following a power-law relationship. Our findings show that the dynamic behavior of rumor models is much richer than shown in previous investigations. Rumors and information spreading emerge naturally from human-to-human interaction and have a growing impact on people’s lives due to increasing and faster access to information, whether trustworthy or not. The authors study the Maki–Thompson rumor model and its variation, revealing a phase transition and providing insights into the nature of this transition.
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21
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Investigating the efficiency of dynamic vaccination by consolidating detecting errors and vaccine efficacy. Sci Rep 2022; 12:8111. [PMID: 35581274 PMCID: PMC9114144 DOI: 10.1038/s41598-022-12039-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/01/2021] [Accepted: 05/05/2022] [Indexed: 11/30/2022] Open
Abstract
Vaccination, if available, is the best preventive measure against infectious diseases. It is, however, needed to prudently design vaccination strategies to successfully mitigate the disease spreading, especially in a time when vaccine scarcity is inevitable. Here we investigate a vaccination strategy on a scale-free network where susceptible individuals, who have social connections with infected people, are being detected and given vaccination before having any physical contact with the infected one. Nevertheless, detecting susceptible (also infected ones) may not be perfect due to the lack of information. Also, vaccines do not confer perfect immunity in reality. We incorporate these pragmatic hindrances in our analysis. We find that if vaccines are highly efficacious, and the detecting error is low, then it is possible to confine the disease spreading—by administering a less amount of vaccination—within a short period. In a situation where tracing susceptible seems difficult, then expanding the range for vaccination targets can be socially advantageous only if vaccines are effective enough. Our analysis further reveals that a more frequent screening for vaccination can reduce the effect of detecting errors. In the end, we present a link percolation-based analytic method to approximate the results of our simulation.
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22
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Hohenegger S, Cacciapaglia G, Sannino F. Effective mathematical modelling of health passes during a pandemic. Sci Rep 2022; 12:6989. [PMID: 35484143 PMCID: PMC9049016 DOI: 10.1038/s41598-022-10663-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Accepted: 03/30/2022] [Indexed: 11/09/2022] Open
Abstract
We study the impact on the epidemiological dynamics of a class of restrictive measures that are aimed at reducing the number of contacts of individuals who have a higher risk of being infected with a transmittable disease. Such measures are currently either implemented or at least discussed in numerous countries worldwide to ward off a potential new wave of COVID-19. They come in the form of Health Passes (HP), which grant full access to public life only to individuals with a certificate that proves that they have either been fully vaccinated, have recovered from a previous infection or have recently tested negative to SARS-Cov-2. We develop both a compartmental model as well as an epidemic Renormalisation Group approach, which is capable of describing the dynamics over a longer period of time, notably an entire epidemiological wave. Introducing different versions of HPs in this model, we are capable of providing quantitative estimates on the effectiveness of the underlying measures as a function of the fraction of the population that is vaccinated and the vaccination rate. We apply our models to the latest COVID-19 wave in several European countries, notably Germany and Austria, which validate our theoretical findings.
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Affiliation(s)
- Stefan Hohenegger
- Institut de Physique des 2 Infinis (IP2I) de Lyon, CNRS/IN2P3, UMR5822, 69622, Villeurbanne, France
- Université de Lyon, Université Claude Bernard Lyon 1, 69001, Lyon, France
| | - Giacomo Cacciapaglia
- Institut de Physique des 2 Infinis (IP2I) de Lyon, CNRS/IN2P3, UMR5822, 69622, Villeurbanne, France.
- Université de Lyon, Université Claude Bernard Lyon 1, 69001, Lyon, France.
| | - Francesco Sannino
- Scuola Superiore Meridionale, Largo S. Marcellino, 10, 80138, Naples, NA, Italy
- Dipartimento di Fisica, E. Pancini, Università di Napoli, Federico II and INFN sezione di Napoli, Complesso Universitario di Monte S. Angelo Edificio 6, via Cintia, 80126, Naples, Italy
- CP3-Origins and D-IAS, University of Southern Denmark, Campusvej 55, 5230, Odense, Denmark
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23
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Rizi AK, Faqeeh A, Badie-Modiri A, Kivelä M. Epidemic spreading and digital contact tracing: Effects of heterogeneous mixing and quarantine failures. Phys Rev E 2022; 105:044313. [PMID: 35590624 DOI: 10.1103/physreve.105.044313] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/07/2021] [Accepted: 03/22/2022] [Indexed: 06/15/2023]
Abstract
Contact tracing via digital tracking applications installed on mobile phones is an important tool for controlling epidemic spreading. Its effectivity can be quantified by modifying the standard methodology for analyzing percolation and connectivity of contact networks. We apply this framework to networks with varying degree distributions, numbers of application users, and probabilities of quarantine failures. Further, we study structured populations with homophily and heterophily and the possibility of degree-targeted application distribution. Our results are based on a combination of explicit simulations and mean-field analysis. They indicate that there can be major differences in the epidemic size and epidemic probabilities which are equivalent in the normal susceptible-infectious-recovered (SIR) processes. Further, degree heterogeneity is seen to be especially important for the epidemic threshold but not as much for the epidemic size. The probability that tracing leads to quarantines is not as important as the application adoption rate. Finally, both strong homophily and especially heterophily with regard to application adoption can be detrimental. Overall, epidemic dynamics are very sensitive to all of the parameter values we tested out, which makes the problem of estimating the effect of digital contact tracing an inherently multidimensional problem.
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Affiliation(s)
- Abbas K Rizi
- Department of Computer Science, School of Science, Aalto University, FI-00076, Finland
| | - Ali Faqeeh
- Department of Computer Science, School of Science, Aalto University, FI-00076, Finland
- Mathematics Applications Consortium for Science & Industry, University of Limerick, Limerick V94 T9PX, Ireland
- Luddy School of Informatics, Computing, and Engineering, Indiana University, Bloomington, Indiana 47408, USA
| | - Arash Badie-Modiri
- Department of Computer Science, School of Science, Aalto University, FI-00076, Finland
| | - Mikko Kivelä
- Department of Computer Science, School of Science, Aalto University, FI-00076, Finland
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24
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Carollo F, Lesanovsky I. Nonequilibrium Dark Space Phase Transition. PHYSICAL REVIEW LETTERS 2022; 128:040603. [PMID: 35148125 DOI: 10.1103/physrevlett.128.040603] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2021] [Revised: 09/22/2021] [Accepted: 01/06/2022] [Indexed: 06/14/2023]
Abstract
We introduce the concept of dark space phase transition, which may occur in open many-body quantum systems where irreversible decay, interactions, and quantum interference compete. Our study is based on a quantum many-body model that is inspired by classical nonequilibrium processes which feature phase transitions into an absorbing state, such as epidemic spreading. The possibility for different dynamical paths to interfere quantum mechanically results in collective dynamical behavior without classical counterpart. We identify two competing dark states, a trivial one corresponding to a classical absorbing state and an emergent one which is quantum coherent. We establish a nonequilibrium phase transition within this dark space that features a phenomenology which cannot be encountered in classical systems. Such emergent two-dimensional dark space may find technological applications, e.g., for the collective encoding of a quantum information.
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Affiliation(s)
- Federico Carollo
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
| | - Igor Lesanovsky
- Institut für Theoretische Physik, Eberhard Karls Universität Tübingen, Auf der Morgenstelle 14, 72076 Tübingen, Germany
- School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, The University of Nottingham, Nottingham NG7 2RD, United Kingdom
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25
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Baumgarten L, Bornholdt S. Epidemics with asymptomatic transmission: Subcritical phase from recursive contact tracing. Phys Rev E 2021; 104:054310. [PMID: 34942758 DOI: 10.1103/physreve.104.054310] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/27/2020] [Accepted: 11/16/2021] [Indexed: 11/07/2022]
Abstract
The challenges presented by the COVID-19 epidemic have created a renewed interest in the development of new methods to combat infectious diseases, and it has shown the importance of preparedness for possible future diseases. A prominent property of the SARS-CoV-2 transmission is the significant fraction of asymptomatic transmission. This may influence the effectiveness of the standard contact tracing procedure for quarantining potentially infected individuals. However, the effects of asymptomatic transmission on the epidemic threshold of epidemic spreading on networks have rarely been studied explicitly. Here we study the critical percolation transition for an arbitrary disease with a nonzero asymptomatic rate in a simple epidemic network model in the presence of a recursive contact tracing algorithm for instant quarantining. We find that, above a certain fraction of asymptomatic transmission, standard contact tracing loses its ability to suppress spreading below the epidemic threshold. However, we also find that recursive contact tracing opens a possibility to contain epidemics with a large fraction of asymptomatic or presymptomatic transmission. In particular, we calculate the required fraction of network nodes participating in the contact tracing for networks with arbitrary degree distributions and for varying recursion depths and discuss the influence of recursion depth and asymptomatic rate on the epidemic percolation phase transition. We anticipate recursive contact tracing to provide a basis for digital, app-based contact tracing tools that extend the efficiency of contact tracing to diseases with a large fraction of asymptomatic transmission.
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Affiliation(s)
- Lorenz Baumgarten
- Institut für Theoretische Physik, Universität Bremen, 28759 Bremen, Germany
| | - Stefan Bornholdt
- Institut für Theoretische Physik, Universität Bremen, 28759 Bremen, Germany
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26
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Wang Y, Zhao Y, Pan Q. Advances, challenges and opportunities of phylogenetic and social network analysis using COVID-19 data. Brief Bioinform 2021; 23:6380452. [PMID: 34601563 DOI: 10.1093/bib/bbab406] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Revised: 08/04/2021] [Accepted: 09/03/2021] [Indexed: 11/15/2022] Open
Abstract
Coronavirus disease 2019 (COVID-19) has attracted research interests from all fields. Phylogenetic and social network analyses based on connectivity between either COVID-19 patients or geographic regions and similarity between syndrome coronavirus 2 (SARS-CoV-2) sequences provide unique angles to answer public health and pharmaco-biological questions such as relationships between various SARS-CoV-2 mutants, the transmission pathways in a community and the effectiveness of prevention policies. This paper serves as a systematic review of current phylogenetic and social network analyses with applications in COVID-19 research. Challenges in current phylogenetic network analysis on SARS-CoV-2 such as unreliable inferences, sampling bias and batch effects are discussed as well as potential solutions. Social network analysis combined with epidemiology models helps to identify key transmission characteristics and measure the effectiveness of prevention and control strategies. Finally, future new directions of network analysis motivated by COVID-19 data are summarized.
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Affiliation(s)
- Yue Wang
- School of Mathematical and Natural Science, Arizona State University, 4701 W Thunderbird Rd, 85306, Arizona, USA
| | - Yunpeng Zhao
- School of Mathematical and Natural Science, Arizona State University, 4701 W Thunderbird Rd, 85306, Arizona, USA
| | - Qing Pan
- Department of Statistics, George Washington University, 801 22nd St. NW, 20052, Washington DC, USA
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27
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Penney MD, Yargic Y, Smolin L, Thommes EW, Anand M, Bauch CT. "Hot-spotting" to improve vaccine allocation by harnessing digital contact tracing technology: An application of percolation theory. PLoS One 2021; 16:e0256889. [PMID: 34551000 PMCID: PMC8457469 DOI: 10.1371/journal.pone.0256889] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2021] [Accepted: 08/17/2021] [Indexed: 11/18/2022] Open
Abstract
Vaccinating individuals with more exposure to others can be disproportionately effective, in theory, but identifying these individuals is difficult and has long prevented implementation of such strategies. Here, we propose how the technology underlying digital contact tracing could be harnessed to boost vaccine coverage among these individuals. In order to assess the impact of this "hot-spotting" proposal we model the spread of disease using percolation theory, a collection of analytical techniques from statistical physics. Furthermore, we introduce a novel measure which we call the efficiency, defined as the percentage decrease in the reproduction number per percentage of the population vaccinated. We find that optimal implementations of the proposal can achieve herd immunity with as little as half as many vaccine doses as a non-targeted strategy, and is attractive even for relatively low rates of app usage.
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Affiliation(s)
- Mark D. Penney
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
| | - Yigit Yargic
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
- Department of Physics and Astronomy, University of Waterloo, Waterloo, Ontario, Canada
| | - Lee Smolin
- Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
| | - Edward W. Thommes
- Vaccine Epidemiology and Modeling, Sanofi Pasteur, Toronto, Ontario, Canada
- Department of Mathematics and Statistics, University of Guelph, Guelph, Ontario, Canada
- Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada
| | - Madhur Anand
- School of Environmental Sciences, University of Guelph, Guelph, Ontario, Canada
| | - Chris T. Bauch
- Department of Applied Mathematics, University of Waterloo, Waterloo, Ontario, Canada
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28
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Critical fluctuations in epidemic models explain COVID-19 post-lockdown dynamics. Sci Rep 2021; 11:13839. [PMID: 34226646 PMCID: PMC8257671 DOI: 10.1038/s41598-021-93366-7] [Citation(s) in RCA: 16] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/15/2021] [Accepted: 06/24/2021] [Indexed: 11/09/2022] Open
Abstract
As the COVID-19 pandemic progressed, research on mathematical modeling became imperative and very influential to understand the epidemiological dynamics of disease spreading. The momentary reproduction ratio r(t) of an epidemic is used as a public health guiding tool to evaluate the course of the epidemic, with the evolution of r(t) being the reasoning behind tightening and relaxing control measures over time. Here we investigate critical fluctuations around the epidemiological threshold, resembling new waves,
even when the community disease transmission rate \documentclass[12pt]{minimal}
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\begin{document}$$\beta$$\end{document}β is not significantly changing. Without loss of generality, we use simple models that can be treated analytically and results are applied to more complex models describing COVID-19 epidemics. Our analysis shows that, rather than the supercritical regime (infectivity larger than a critical value, \documentclass[12pt]{minimal}
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\begin{document}$$\beta > \beta _c$$\end{document}β>βc) leading to new exponential growth of infection, the subcritical regime (infectivity smaller than a critical value, \documentclass[12pt]{minimal}
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\begin{document}$$\beta < \beta _c$$\end{document}β<βc) with small import is able to explain the dynamic behaviour of COVID-19 spreading after a lockdown lifting, with \documentclass[12pt]{minimal}
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\begin{document}$$r(t) \approx 1$$\end{document}r(t)≈1 hovering around its threshold value.
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29
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Campi G, Valletta A, Perali A, Marcelli A, Bianconi A. Epidemic spreading in an expanded parameter space: the supercritical scaling laws and subcritical metastable phases. Phys Biol 2021; 18. [PMID: 34038897 DOI: 10.1088/1478-3975/ac059d] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/10/2021] [Accepted: 05/26/2021] [Indexed: 02/06/2023]
Abstract
While the mathematical laws of uncontrolled epidemic spreading are well known, the statistical physics of coronavirus epidemics with containment measures is currently lacking. The modelling of available data of the first wave of the Covid-19 pandemic in 2020 over 230 days, in different countries representative of different containment policies is relevant to quantify the efficiency of these policies to face the containment of any successive wave. At this aim we have built a 3D phase diagram tracking the simultaneous evolution and the interplay of the doubling time,Td, and the reproductive number,Rtmeasured using the methodological definition used by the Robert Koch Institute. In this expanded parameter space three different main phases,supercritical,criticalandsubcriticalare identified. Moreover, we have found that in thesupercriticalregime withRt> 1 the doubling time is smaller than 40 days. In this phase we have established the power law relation betweenTdand (Rt- 1)-νwith the exponentνdepending on the definition of reproductive number. In thesubcriticalregime whereRt< 1 andTd> 100 days, we have identified arrested metastable phases whereTdis nearly constant.
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Affiliation(s)
- Gaetano Campi
- Institute of Crystallography, CNR, via Salaria Km 29. 300, Monterotondo Stazione, Roma I-00015, Italy.,Rome International Centre Materials Science Superstripes RICMASS via dei Sabelli 119A, 00185 Rome, Italy
| | - Antonio Valletta
- Institute for Microelectronics and Microsystems, IMM, Consiglio Nazionale delle Ricerche CNR Via del Fosso del Cavaliere 100, 00133 Roma, Italy
| | - Andrea Perali
- Rome International Centre Materials Science Superstripes RICMASS via dei Sabelli 119A, 00185 Rome, Italy.,School of Pharmacy, Physics Unit, University of Camerino, 62032 Camerino (MC), Italy
| | - Augusto Marcelli
- Rome International Centre Materials Science Superstripes RICMASS via dei Sabelli 119A, 00185 Rome, Italy.,INFN-Laboratori Nazionali di Frascati, 00044 Frascati (RM), Italy
| | - Antonio Bianconi
- Institute of Crystallography, CNR, via Salaria Km 29. 300, Monterotondo Stazione, Roma I-00015, Italy.,Rome International Centre Materials Science Superstripes RICMASS via dei Sabelli 119A, 00185 Rome, Italy.,National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow, Russia
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30
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Ódor G. Nonuniversal power-law dynamics of susceptible infected recovered models on hierarchical modular networks. Phys Rev E 2021; 103:062112. [PMID: 34271752 DOI: 10.1103/physreve.103.062112] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/18/2021] [Accepted: 05/25/2021] [Indexed: 11/07/2022]
Abstract
Power-law (PL) time-dependent infection growth has been reported in many COVID-19 statistics. In simple susceptible infected recovered (SIR) models, the number of infections grows at the outbreak as I(t)∝t^{d-1} on d-dimensional Euclidean lattices in the endemic phase, or it follows a slower universal PL at the critical point, until finite sizes cause immunity and a crossover to an exponential decay. Heterogeneity may alter the dynamics of spreading models, and spatially inhomogeneous infection rates can cause slower decays, posing a threat of a long recovery from a pandemic. COVID-19 statistics have also provided epidemic size distributions with PL tails in several countries. Here I investigate SIR-like models on hierarchical modular networks, embedded in 2d lattices with the addition of long-range links. I show that if the topological dimension of the network is finite, average degree-dependent PL growth of prevalence emerges. Supercritically, the same exponents as those of regular graphs occur, but the topological disorder alters the critical behavior. This is also true for the epidemic size distributions. Mobility of individuals does not affect the form of the scaling behavior, except for the d=2 lattice, but it increases the magnitude of the epidemic. The addition of a superspreader hot spot also does not change the growth exponent and the exponential decay in the herd immunity regime.
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Affiliation(s)
- Géza Ódor
- Institute of Technical Physics and Materials Science, Center for Energy Research, P.O. Box 49, H-1525 Budapest, Hungary
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31
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Ariel G, Louzoun Y. Self-driven criticality in a stochastic epidemic model. Phys Rev E 2021; 103:062303. [PMID: 34271622 DOI: 10.1103/physreve.103.062303] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2021] [Accepted: 05/18/2021] [Indexed: 11/06/2022]
Abstract
We present a generic epidemic model with stochastic parameters in which the dynamics self-organize to a critical state with suppressed exponential growth. More precisely, the dynamics evolve into a quasi-steady state, where the effective reproduction rate fluctuates close to the critical value 1 for a long period, as indeed observed for different epidemics. The main assumptions underlying the model are that the rate at which each individual becomes infected changes stochastically in time with a heavy-tailed steady state. The critical regime is characterized by an extremely long duration of the epidemic. Its stability is analyzed both numerically and analytically in different models.
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Affiliation(s)
- Gil Ariel
- Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel
| | - Yoram Louzoun
- Department of Mathematics, Bar-Ilan University, Ramat Gan 52900, Israel
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32
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Rosales Herrera D, Ramírez JE, Martínez MI, Cruz-Suárez H, Fernández Téllez A, López-Olguín JF, Aragón García A. Percolation-intercropping strategies to prevent dissemination of phytopathogens on plantations. CHAOS (WOODBURY, N.Y.) 2021; 31:063105. [PMID: 34241313 DOI: 10.1063/5.0044714] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2021] [Accepted: 04/05/2021] [Indexed: 06/13/2023]
Abstract
Phytophthora is one of the most aggressive and worldwide extended phytopathogens that attack plants and trees. Its effects produce tremendous economical losses in agronomy and forestry since no effective fungicide exists. We propose to combine percolation theory with an intercropping sowing configuration as a non-chemical strategy to minimize the dissemination of the pathogen. In this work, we model a plantation as a square lattice where two types of plants are arranged in alternating columns or diagonals, and Phytophthora zoospores are allowed to propagate to the nearest and next-to-nearest neighboring plants. We determine the percolation threshold for each intercropping configuration as a function of the plant's susceptibilities and the number of inoculated cells at the beginning of the propagation process. The results are presented as phase diagrams where crop densities that prevent the formation of a spanning cluster of susceptible or diseased plants are indicated. The main result is the existence of susceptibility value combinations for which no spanning cluster is formed even if every cell in the plantation is sowed. This finding can be useful in choosing a configuration and density of plants that minimize damages caused by Phytophthora. We illustrate the application of the phase diagrams with the susceptibilities of three plants with a high commercial value.
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Affiliation(s)
- Diana Rosales Herrera
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico
| | - J E Ramírez
- Centro de Agroecología, Instituto de Ciencias, Benemérita Universidad Autónoma de Puebla, Edificio VAL 1 - Ecocampus Valsequillo, Km 1.7 carretera a San Baltazar Tetela, San Pedro Zacachimalpa, 72960, Puebla, Puebla, Mexico
| | - M I Martínez
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico
| | - H Cruz-Suárez
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico
| | - A Fernández Téllez
- Facultad de Ciencias Físico Matemáticas, Benemérita Universidad Autónoma de Puebla, Apartado Postal 165, 72000 Puebla, Puebla, Mexico
| | - Jesús F López-Olguín
- Centro de Agroecología, Instituto de Ciencias, Benemérita Universidad Autónoma de Puebla, Edificio VAL 1 - Ecocampus Valsequillo, Km 1.7 carretera a San Baltazar Tetela, San Pedro Zacachimalpa, 72960, Puebla, Puebla, Mexico
| | - Agustín Aragón García
- Centro de Agroecología, Instituto de Ciencias, Benemérita Universidad Autónoma de Puebla, Edificio VAL 1 - Ecocampus Valsequillo, Km 1.7 carretera a San Baltazar Tetela, San Pedro Zacachimalpa, 72960, Puebla, Puebla, Mexico
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33
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Vassallo L, Di Muro MA, Sarkar D, Valdez LD, Braunstein LA. Ring vaccination strategy in networks: A mixed percolation approach. Phys Rev E 2021; 101:052309. [PMID: 32575220 DOI: 10.1103/physreve.101.052309] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2020] [Accepted: 04/20/2020] [Indexed: 11/06/2022]
Abstract
Ring vaccination is a mitigation strategy that consists in seeking and vaccinating the contacts of a sick patient, in order to provide immunization and halt the spread of disease. We study an extension of the susceptible-infected-recovered (SIR) epidemic model with ring vaccination in complex and spatial networks. Previously, a correspondence between this model and a link percolation process has been established, however, this is only valid in complex networks. Here, we propose that the SIR model with ring vaccination is equivalent to a mixed percolation process of links and nodes, which offers a more complete description of the process. We verify that this approach is valid in both complex and spatial networks, the latter being built according to the Waxman model. This model establishes a distance-dependent cost of connection between individuals arranged in a square lattice. We determine the epidemic-free regions in a phase diagram based on the wiring cost and the parameters of the epidemic model (vaccination and infection probabilities and recovery time). In addition, we find that for long recovery times this model maps into a pure node percolation process, in contrast to the SIR model without ring vaccination, which maps into link percolation.
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Affiliation(s)
- Lautaro Vassallo
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET) and Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, 7600 Mar del Plata, Argentina
| | - Matías A Di Muro
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET) and Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, 7600 Mar del Plata, Argentina
| | - Debmalya Sarkar
- Department of Information and Communication Technology, Manipal Institute of Technology, Manipal Academy of Higher Education, Manipal 576104, India
| | - Lucas D Valdez
- Physics Department, Boston University, Boston, Massachusetts 02215, USA
| | - Lidia A Braunstein
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR-CONICET) and Departamento de Física, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Mar del Plata, 7600 Mar del Plata, Argentina.,Physics Department, Boston University, Boston, Massachusetts 02215, USA
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Tkachenko AV, Maslov S, Elbanna A, Wong GN, Weiner ZJ, Goldenfeld N. Time-dependent heterogeneity leads to transient suppression of the COVID-19 epidemic, not herd immunity. Proc Natl Acad Sci U S A 2021; 118:e2015972118. [PMID: 33833080 PMCID: PMC8092384 DOI: 10.1073/pnas.2015972118] [Citation(s) in RCA: 35] [Impact Index Per Article: 11.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022] Open
Abstract
Epidemics generally spread through a succession of waves that reflect factors on multiple timescales. On short timescales, superspreading events lead to burstiness and overdispersion, whereas long-term persistent heterogeneity in susceptibility is expected to lead to a reduction in both the infection peak and the herd immunity threshold (HIT). Here, we develop a general approach to encompass both timescales, including time variations in individual social activity, and demonstrate how to incorporate them phenomenologically into a wide class of epidemiological models through reparameterization. We derive a nonlinear dependence of the effective reproduction number [Formula: see text] on the susceptible population fraction S. We show that a state of transient collective immunity (TCI) emerges well below the HIT during early, high-paced stages of the epidemic. However, this is a fragile state that wanes over time due to changing levels of social activity, and so the infection peak is not an indication of long-lasting herd immunity: Subsequent waves may emerge due to behavioral changes in the population, driven by, for example, seasonal factors. Transient and long-term levels of heterogeneity are estimated using empirical data from the COVID-19 epidemic and from real-life face-to-face contact networks. These results suggest that the hardest hit areas, such as New York City, have achieved TCI following the first wave of the epidemic, but likely remain below the long-term HIT. Thus, in contrast to some previous claims, these regions can still experience subsequent waves.
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Affiliation(s)
- Alexei V Tkachenko
- Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, NY 11973;
| | - Sergei Maslov
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801;
- Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
- Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801
| | - Ahmed Elbanna
- Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801
- Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, Urbana, IL 61801
| | - George N Wong
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801
| | - Zachary J Weiner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801
| | - Nigel Goldenfeld
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, IL 61801
- Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, IL 61801
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35
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Federbush A, Kantor Y. Percolation perspective on sites not visited by a random walk in two dimensions. Phys Rev E 2021; 103:032137. [PMID: 33862701 DOI: 10.1103/physreve.103.032137] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/27/2020] [Accepted: 02/26/2021] [Indexed: 11/07/2022]
Abstract
We consider the percolation problem of sites on an L×L square lattice with periodic boundary conditions which were unvisited by a random walk of N=uL^{2} steps, i.e., are vacant. Most of the results are obtained from numerical simulations. Unlike its higher-dimensional counterparts, this problem has no sharp percolation threshold and the spanning (percolation) probability is a smooth function monotonically decreasing with u. The clusters of vacant sites are not fractal but have fractal boundaries of dimension 4/3. The lattice size L is the only large length scale in this problem. The typical mass (number of sites s) in the largest cluster is proportional to L^{2}, and the mean mass of the remaining (smaller) clusters is also proportional to L^{2}. The normalized (per site) density n_{s} of clusters of size (mass) s is proportional to s^{-τ}, while the volume fraction P_{k} occupied by the kth largest cluster scales as k^{-q}. We put forward a heuristic argument that τ=2 and q=1. However, the numerically measured values are τ≈1.83 and q≈1.20. We suggest that these are effective exponents that drift towards their asymptotic values with increasing L as slowly as 1/lnL approaches zero.
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Affiliation(s)
- Amit Federbush
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
| | - Yacov Kantor
- Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, Tel Aviv 69978, Israel
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36
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Klocke K, Wintermantel TM, Lochead G, Whitlock S, Buchhold M. Hydrodynamic Stabilization of Self-Organized Criticality in a Driven Rydberg Gas. PHYSICAL REVIEW LETTERS 2021; 126:123401. [PMID: 33834799 DOI: 10.1103/physrevlett.126.123401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/29/2020] [Accepted: 02/18/2021] [Indexed: 06/12/2023]
Abstract
Signatures of self-organized criticality (SOC) have recently been observed in an ultracold atomic gas under continuous laser excitation to strongly interacting Rydberg states [S. Helmrich et al., Nature, 577, 481-486 (2020)]. This creates unique possibilities to study this intriguing dynamical phenomenon under controlled experimental conditions. Here we theoretically and experimentally examine the self-organizing dynamics of a driven ultracold gas and identify an unanticipated feedback mechanism originating from the interaction of the system with a thermal reservoir. Transport of particles from the flanks of the cloud toward the center compensates avalanche-induced atom loss. This mechanism sustains an extended critical region in the trap center for timescales much longer than the initial self-organization dynamics. The characteristic flattop density profile provides an additional experimental signature for SOC while simultaneously enabling studies of SOC under almost homogeneous conditions. We present a hydrodynamic description for the reorganization of the atom density, which very accurately describes the experimentally observed features on intermediate and long timescales, and which is applicable to both collisional hydrodynamic and chaotic ballistic regimes.
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Affiliation(s)
- K Klocke
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Department of Physics, University of California, Berkeley, California 94720, USA
| | - T M Wintermantel
- ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
- Physikalisches Institut, Universität Heidelberg, 69120 Heidelberg, Germany
| | - G Lochead
- ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - S Whitlock
- ISIS (UMR 7006), University of Strasbourg and CNRS, 67000 Strasbourg, France
| | - M Buchhold
- Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA
- Institut für Theoretische Physik, Universität zu Köln, D-50937 Cologne, Germany
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37
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Alexiadis A, Albano A, Rahmat A, Yildiz M, Kefal A, Ozbulut M, Bakirci N, Garzón-Alvarado DA, Duque-Daza CA, Eslava-Schmalbach JH. Simulation of pandemics in real cities: enhanced and accurate digital laboratories. Proc Math Phys Eng Sci 2021; 477:20200653. [PMID: 33633493 PMCID: PMC7897638 DOI: 10.1098/rspa.2020.0653] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Accepted: 12/14/2020] [Indexed: 12/28/2022] Open
Abstract
This study develops a modelling framework for simulating the spread of infectious diseases within real cities. Digital copies of Birmingham (UK) and Bogotá (Colombia) are generated, reproducing their urban environment, infrastructure and population. The digital inhabitants have the same statistical features of the real population. Their motion is a combination of predictable trips (commute to work, school, etc.) and random walks (shopping, leisure, etc.). Millions of individuals, their encounters and the spread of the disease are simulated by means of high-performance computing and massively parallel algorithms for several months and a time resolution of 1 minute. Simulations accurately reproduce the COVID-19 data for Birmingham and Bogotá both before and during the lockdown. The model has only one adjustable parameter calculable in the early stages of the pandemic. Policymakers can use our digital cities as virtual laboratories for testing, predicting and comparing the effects of policies aimed at containing epidemics.
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Affiliation(s)
- A Alexiadis
- School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
| | - A Albano
- School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
| | - A Rahmat
- School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK
| | - M Yildiz
- Faculty of Engineering and Natural Sciences, Sabanci University, 34956 Tuzla, Istanbul, Turkey
| | - A Kefal
- Faculty of Engineering and Natural Sciences, Sabanci University, 34956 Tuzla, Istanbul, Turkey
| | - M Ozbulut
- Faculty of Engineering, Piri Reis University, 34940 Istanbul, Turkey
| | - N Bakirci
- School of Medicine, Acibadem University, lçerenköy, Kayışdağı 32, 34684 Istanbul, Turkey
| | - D A Garzón-Alvarado
- Department of Mechanical and Mechatronic Engineering, Universidad Nacional de Colombia, Cra 30 No 45-03. Bogotá, Colombia
| | - C A Duque-Daza
- School of Chemical Engineering, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK.,Department of Mechanical and Mechatronic Engineering, Universidad Nacional de Colombia, Cra 30 No 45-03. Bogotá, Colombia
| | - J H Eslava-Schmalbach
- School of Medicine, Universidad Nacional de Colombia, Hospital Universitario Nacional de Colombia, Cra 30 No 45-03. Bogotá, Colombia
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38
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Epidemic growth and Griffiths effects on an emergent network of excited atoms. Nat Commun 2021; 12:103. [PMID: 33397997 PMCID: PMC7782709 DOI: 10.1038/s41467-020-20333-7] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2020] [Accepted: 11/16/2020] [Indexed: 12/04/2022] Open
Abstract
Whether it be physical, biological or social processes, complex systems exhibit dynamics that are exceedingly difficult to understand or predict from underlying principles. Here we report a striking correspondence between the excitation dynamics of a laser driven gas of Rydberg atoms and the spreading of diseases, which in turn opens up a controllable platform for studying non-equilibrium dynamics on complex networks. The competition between facilitated excitation and spontaneous decay results in sub-exponential growth of the excitation number, which is empirically observed in real epidemics. Based on this we develop a quantitative microscopic susceptible-infected-susceptible model which links the growth and final excitation density to the dynamics of an emergent heterogeneous network and rare active region effects associated to an extended Griffiths phase. This provides physical insights into the nature of non-equilibrium criticality in driven many-body systems and the mechanisms leading to non-universal power-laws in the dynamics of complex systems. The emergent excitation dynamics of an ultracold gas of Rydberg atoms exhibits features analogous to epidemic spreading on networks. Wintermantel et al. propose a controllable experimental system for studying network dynamics at the interface of mathematical models and real-world complex systems.
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39
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Ghanbari A, Khordad R, Ghaderi-Zefrehei M. Mathematical prediction of the spreading rate of COVID-19 using entropy-based thermodynamic model. INDIAN JOURNAL OF PHYSICS AND PROCEEDINGS OF THE INDIAN ASSOCIATION FOR THE CULTIVATION OF SCIENCE (2004) 2021; 95:2567-2573. [PMID: 33424191 PMCID: PMC7778492 DOI: 10.1007/s12648-020-01930-0] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/12/2020] [Accepted: 09/16/2020] [Indexed: 05/09/2023]
Abstract
In the COVID-19 pandemic era, undoubtedly mathematical modeling helps epidemiological scientists and authorities to take informing decisions about pandemic planning, wise resource allocation, introducing relevant non-pharmaceutical interventions and implementation of social distancing measures. The current coronavirus disease (COVID-19) emerged in the end of 2019, Wuhan, China, spreads quickly in the world. In this study, an entropy-based thermodynamic model has been used for predicting and spreading the rate of COVID-19. In our model, all the epidemic details were considered into a single time-dependent parameter. The parameter was analytically determined using four constraints, including the existence of an inflexion point and a maximum value. Our model has been layout-based the Shannon entropy and the maximum rate of entropy production of postulated complex system. The results show that our proposed model fits well with the number of confirmed COVID-19 cases in daily basis. Also, as a matter of fact that Shannon entropy is an intersection of information, probability theory, (non)linear dynamical systems and statistical physics, the proposed model in this study can be further calibrated to fit much better on COVID-19 observational data, using the above formalisms.
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Affiliation(s)
- A. Ghanbari
- Department of Physics, College of Science, Yasouj University, Yasouj, 75918-74934 Iran
| | - R. Khordad
- Department of Physics, College of Science, Yasouj University, Yasouj, 75918-74934 Iran
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40
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Wada AHO, Hoyos JA. Critical properties of the susceptible-exposed-infected model with correlated temporal disorder. Phys Rev E 2021; 103:012306. [PMID: 33601627 DOI: 10.1103/physreve.103.012306] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/24/2020] [Accepted: 01/04/2021] [Indexed: 06/12/2023]
Abstract
In this paper we study the critical properties of the nonequilibrium phase transition of the susceptible-exposed-infected (SEI) model under the effects of long-range correlated time-varying environmental noise on the Bethe lattice. We show that temporal noise is perturbatively relevant changing the universality class from the (mean-field) dynamical percolation to the exotic infinite-noise universality class of the contact process model. Our analytical results are based on a mapping to the one-dimensional fractional Brownian motion with an absorbing wall and is confirmed by Monte Carlo simulations. Unlike the contact process, our theory also predicts that it is quite difficult to observe the associated active temporal Griffiths phase in the long-time limit. Finally, we also show an equivalence between the infinite-noise and the compact directed percolation universality classes by relating the SEI model in the presence of temporal disorder to the Domany-Kinzel cellular automaton in the limit of compact clusters.
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Affiliation(s)
- Alexander H O Wada
- Instituto de Física de São Carlos, Universidade de São Paulo, C. P. 369, São Carlos, São Paulo 13560-970, Brazil
| | - José A Hoyos
- Instituto de Física de São Carlos, Universidade de São Paulo, C. P. 369, São Carlos, São Paulo 13560-970, Brazil
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41
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Gross B, Havlin S. Epidemic spreading and control strategies in spatial modular network. APPLIED NETWORK SCIENCE 2020; 5:95. [PMID: 33263074 PMCID: PMC7689394 DOI: 10.1007/s41109-020-00337-4] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 08/03/2020] [Accepted: 11/11/2020] [Indexed: 06/12/2023]
Abstract
Epidemic spread on networks is one of the most studied dynamics in network science and has important implications in real epidemic scenarios. Nonetheless, the dynamics of real epidemics and how it is affected by the underline structure of the infection channels are still not fully understood. Here we apply the susceptible-infected-recovered model and study analytically and numerically the epidemic spread on a recently developed spatial modular model imitating the structure of cities in a country. The model assumes that inside a city the infection channels connect many different locations, while the infection channels between cities are less and usually directly connect only a few nearest neighbor cities in a two-dimensional plane. We find that the model experience two epidemic transitions. The first lower threshold represents a local epidemic spread within a city but not to the entire country and the second higher threshold represents a global epidemic in the entire country. Based on our analytical solution we proposed several control strategies and how to optimize them. We also show that while control strategies can successfully control the disease, early actions are essentials to prevent the disease global spread.
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Affiliation(s)
- Bnaya Gross
- Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
| | - Shlomo Havlin
- Department of Physics, Bar-Ilan University, 52900 Ramat-Gan, Israel
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42
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Saha S, Mishra A, Dana SK, Hens C, Bairagi N. Infection spreading and recovery in a square lattice. Phys Rev E 2020; 102:052307. [PMID: 33327064 DOI: 10.1103/physreve.102.052307] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/05/2020] [Accepted: 10/20/2020] [Indexed: 06/12/2023]
Abstract
We investigate spreading and recovery of disease in a square lattice, and, in particular, emphasize the role of the initial distribution of infected patches in the network on the progression of an endemic and initiation of a recovery process, if any, due to migration of both the susceptible and infected hosts. The disease starts in the lattice with three possible initial distribution patterns of infected and infection-free sites, viz., infected core patches (ICP), infected peripheral patches (IPP), and randomly distributed infected patches (RDIP). Our results show that infection spreads monotonically in the lattice with increasing migration without showing any sign of recovery in the ICP case. In the IPP case, it follows a similar monotonic progression with increasing migration; however, a self-organized healing process starts for higher migration, leading the lattice to full recovery at a critical rate of migration. Encouragingly, for the initial RDIP arrangement, chances of recovery are much higher with a lower rate of critical migration. An eigenvalue-based semianalytical study is made to determine the critical migration rate for realizing a stable infection-free lattice. The initial fraction of infected patches and the force of infection play significant roles in the self-organized recovery. They follow an exponential law, for the RDIP case, that governs the recovery process. For the frustrating case of ICP arrangement, we propose a random rewiring of links in the lattice allowing long-distance migratory paths that effectively initiate a recovery process. Global prevalence of infection thereby declines and progressively improves with the rewiring probability that follows a power law with the critical migration and leads to the birth of emergent infection-free networks.
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Affiliation(s)
- Suman Saha
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
- Translational Health Science and Technology Institute, NCR Biotech Science Cluster 3rd Milestone, Faridabad 121001, India
| | - Arindam Mishra
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Syamal K Dana
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
| | - Chittaranjan Hens
- Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata 700108, India
| | - Nandadulal Bairagi
- Centre for Mathematical Biology and Ecology, Department of Mathematics, Jadavpur University, Kolkata 700032, India
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43
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Müller M, Derlet PM, Mudry C, Aeppli G. Testing of asymptomatic individuals for fast feedback-control of COVID-19 pandemic. Phys Biol 2020; 17:065007. [PMID: 33048841 DOI: 10.1088/1478-3975/aba6d0] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Abstract
We argue that frequent sampling of the fraction of a priori non-symptomatic but infectious humans (either by random or cohort testing) significantly improves the management of the COVID-19 pandemic, when compared to intervention strategies relying on data from symptomatic cases only. This is because such sampling measures the incidence of the disease, the key variable controlled by restrictive measures, and thus anticipates the load on the healthcare system due to progression of the disease. The frequent testing of non-symptomatic infectiousness will (i) significantly improve the predictability of the pandemic, (ii) allow informed and optimized decisions on how to modify restrictive measures, with shorter delay times than the present ones, and (iii) enable the real-time assessment of the efficiency of new means to reduce transmission rates. These advantages are quantified by considering a feedback and control model of mitigation where the feedback is derived from the evolution of the daily measured prevalence. While the basic model we propose aggregates data for the entire population of a country such as Switzerland, we point out generalizations which account for hot spots which are analogous to Anderson-localized regions in the theory of diffusion in random media.
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Affiliation(s)
- Markus Müller
- Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
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44
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Jorritsma J, Hulshof T, Komjáthy J. Not all interventions are equal for the height of the second peak. CHAOS, SOLITONS, AND FRACTALS 2020; 139:109965. [PMID: 32863609 PMCID: PMC7445132 DOI: 10.1016/j.chaos.2020.109965] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/29/2020] [Accepted: 06/02/2020] [Indexed: 05/24/2023]
Abstract
In this paper we conduct a simulation study of the spread of an epidemic like COVID-19 with temporary immunity on finite spatial and non-spatial network models. In particular, we assume that an epidemic spreads stochastically on a scale-free network and that each infected individual in the network gains a temporary immunity after its infectious period is over. After the temporary immunity period is over, the individual becomes susceptible to the virus again. When the underlying contact network is embedded in Euclidean geometry, we model three different intervention strategies that aim to control the spread of the epidemic: social distancing, restrictions on travel, and restrictions on maximal number of social contacts per node. Our first finding is that on a finite network, a long enough average immunity period leads to extinction of the pandemic after the first peak, analogous to the concept of "herd immunity". For each model, there is a critical average immunity duration Lc above which this happens. Our second finding is that all three interventions manage to flatten the first peak (the travel restrictions most efficiently), as well as decrease the critical immunity duration Lc , but elongate the epidemic. However, when the average immunity duration L is shorter than Lc , the price for the flattened first peak is often a high second peak: for limiting the maximal number of contacts, the second peak can be as high as 1/3 of the first peak, and twice as high as it would be without intervention. Thirdly, interventions introduce oscillations into the system and the time to reach equilibrium is, for almost all scenarios, much longer. We conclude that network-based epidemic models can show a variety of behaviors that are not captured by the continuous compartmental models.
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Affiliation(s)
- Joost Jorritsma
- Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
| | | | - Júlia Komjáthy
- Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
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Perez IA, Di Muro MA, La Rocca CE, Braunstein LA. Disease spreading with social distancing: A prevention strategy in disordered multiplex networks. Phys Rev E 2020; 102:022310. [PMID: 32942454 DOI: 10.1103/physreve.102.022310] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/21/2020] [Accepted: 08/03/2020] [Indexed: 11/07/2022]
Abstract
The frequent emergence of diseases with the potential to become threats at local and global scales, such as influenza A(H1N1), SARS, MERS, and recently COVID-19 disease, makes it crucial to keep designing models of disease propagation and strategies to prevent or mitigate their effects in populations. Since isolated systems are exceptionally rare to find in any context, especially in human contact networks, here we examine the susceptible-infected-recovered model of disease spreading in a multiplex network formed by two distinct networks or layers, interconnected through a fraction q of shared individuals (overlap). We model the interactions through weighted networks, because person-to-person interactions are diverse (or disordered); weights represent the contact times of the interactions. Using branching theory supported by simulations, we analyze a social distancing strategy that reduces the average contact time in both layers, where the intensity of the distancing is related to the topology of the layers. We find that the critical values of the distancing intensities, above which an epidemic can be prevented, increase with the overlap q. Also we study the effect of the social distancing on the mutual giant component of susceptible individuals, which is crucial to keep the functionality of the system. In addition, we find that for relatively small values of the overlap q, social distancing policies might not be needed at all to maintain the functionality of the system.
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Affiliation(s)
- Ignacio A Perez
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata, CONICET, Déan Funes 3350, 7600 Mar del Plata, Argentina
| | - Matías A Di Muro
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata, CONICET, Déan Funes 3350, 7600 Mar del Plata, Argentina
| | - Cristian E La Rocca
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata, CONICET, Déan Funes 3350, 7600 Mar del Plata, Argentina
| | - Lidia A Braunstein
- Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), Departamento de Física, FCEyN, Universidad Nacional de Mar del Plata, CONICET, Déan Funes 3350, 7600 Mar del Plata, Argentina and Physics Department, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA
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Ma J, Valdez LD, Braunstein LA. Role of bridge nodes in epidemic spreading: Different regimes and crossovers. Phys Rev E 2020; 102:032308. [PMID: 33075958 DOI: 10.1103/physreve.102.032308] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/15/2020] [Accepted: 08/31/2020] [Indexed: 11/07/2022]
Abstract
Power-law behaviors are common in many disciplines, especially in network science. Real-world networks, like disease spreading among people, are more likely to be interconnected communities, and show richer power-law behaviors than isolated networks. In this paper, we look at the system of two communities which are connected by bridge links between a fraction r of bridge nodes, and study the effect of bridge nodes to the final state of the Susceptible-Infected-Recovered model by mapping it to link percolation. By keeping a fixed average connectivity, but allowing different transmissibilities along internal and bridge links, we theoretically derive different power-law asymptotic behaviors of the total fraction of the recovered R in the final state as r goes to zero, for different combinations of internal and bridge link transmissibilities. We also find crossover points where R follows different power-law behaviors with r on both sides when the internal transmissibility is below but close to its critical value for different bridge link transmissibilities. All of these power-law behaviors can be explained through different mechanisms of how finite clusters in each community are connected into the giant component of the whole system, and enable us to pick effective epidemic strategies and to better predict their impacts.
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Affiliation(s)
- Jing Ma
- Department of Physics, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA
| | - Lucas D Valdez
- Department of Physics, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA.,Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), FCEyN, Universidad Nacional de Mar del Plata-CONICET, Déan Funes 3350, (7600) Mar del Plata, Argentina
| | - Lidia A Braunstein
- Department of Physics, Boston University, 590 Commonwealth Ave., Boston, Massachusetts 02215, USA.,Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), FCEyN, Universidad Nacional de Mar del Plata-CONICET, Déan Funes 3350, (7600) Mar del Plata, Argentina
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Kühn R, van Mourik J. Heterogeneity in outcomes of repeated instances of percolation experiments. Phys Rev E 2020; 102:032302. [PMID: 33075985 DOI: 10.1103/physreve.102.032302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/24/2020] [Accepted: 08/05/2020] [Indexed: 11/07/2022]
Abstract
We investigate the heterogeneity of outcomes of repeated instances of percolation experiments in complex networks using a message-passing approach to evaluate heterogeneous, node-dependent probabilities of belonging to the giant or percolating cluster, i.e., the set of mutually connected nodes whose size scales linearly with the size of the system. We evaluate these both for large finite single instances and for synthetic networks in the configuration model class in the thermodynamic limit. For the latter, we consider both Erdős-Rényi and scale-free networks as examples of networks with narrow and broad degree distributions, respectively. For real-world networks we use an undirected version of a Gnutella peer-to-peer file-sharing network with N=62568 nodes as an example. We derive the theory for multiple instances of both uncorrelated and correlated percolation processes. For the uncorrelated case, we also obtain a closed-form approximation for the large mean degree limit of Erdős-Rényi networks.
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Affiliation(s)
- Reimer Kühn
- Mathematics Department, King's College London, Strand, London WC2R 2LS,United Kingdom
| | - Jort van Mourik
- NCRG, Aston University, Aston Triangle, Birmingham B4 7ET, United Kingdom
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An Edge-Based Model of SEIR Epidemics on Static Random Networks. Bull Math Biol 2020; 82:96. [PMID: 32676740 DOI: 10.1007/s11538-020-00769-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/13/2019] [Accepted: 06/23/2020] [Indexed: 10/23/2022]
Abstract
Studies have been done using networks to represent the spread of infectious diseases in populations. For diseases with exposed individuals corresponding to a latent period, an SEIR model is formulated using an edge-based approach described by a probability generating function. The basic reproduction number is computed using the next generation matrix method and the final size of the epidemic is derived analytically. The SEIR model in this study is used to investigate the stochasticity of the SEIR dynamics. The stochastic simulations are performed applying continuous-time Gillespie's algorithm given Poisson and power law with exponential cut-off degree distributions. The resulting predictions of the SEIR model given the initial conditions match well with the stochastic simulations, validating the accuracy of the SEIR model. We varied the contribution of the disease parameters and the average degree of the network in order to investigate their effects on the spread of disease. We verified that the infection and the recovery rates show significant effects on the dynamics of the disease transmission. While the exposed rate delays the spread of the disease, increasing it towards infinity would lead to almost the same dynamics as that of an SIR case. A network with high average degree results to an early and higher peak of the epidemic compared to a network with low average degree. The results in this paper can be used as an alternative way of explaining the spread of disease and it provides implications on the control strategies applied to mitigate the disease transmission.
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Kleczkowski A, Hoyle A, McMenemy P. One model to rule them all? Modelling approaches across OneHealth for human, animal and plant epidemics. Philos Trans R Soc Lond B Biol Sci 2020; 374:20180255. [PMID: 31056049 DOI: 10.1098/rstb.2018.0255] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022] Open
Abstract
One hundred years after the 1918 influenza outbreak, are we ready for the next pandemic? This paper addresses the need to identify and develop collaborative, interdisciplinary and cross-sectoral approaches to modelling of infectious diseases including the fields of not only human and veterinary medicine, but also plant epidemiology. Firstly, the paper explains the concepts on which the most common epidemiological modelling approaches are based, namely the division of a host population into susceptible, infected and removed (SIR) classes and the proportionality of the infection rate to the size of the susceptible and infected populations. It then demonstrates how these simple concepts have been developed into a vast and successful modelling framework that has been used in predicting and controlling disease outbreaks for over 100 years. Secondly, it considers the compartmental models based on the SIR paradigm within the broader concept of a 'disease tetrahedron' (comprising host, pathogen, environment and man) and uses it to review the similarities and differences among the fields comprising the 'OneHealth' approach. Finally, the paper advocates interactions between all fields and explores the future challenges facing modellers. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.
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Affiliation(s)
- Adam Kleczkowski
- 1 Department of Mathematics and Statistics, University of Strathclyde , Glasgow G1 1XH , UK
| | - Andy Hoyle
- 2 Computing Science and Mathematics, University of Stirling , Stirling FK9 4LA , UK
| | - Paul McMenemy
- 2 Computing Science and Mathematics, University of Stirling , Stirling FK9 4LA , UK
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Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks. PHYSICAL REVIEW. X 2020. [PMCID: PMC7226907 DOI: 10.1103/physrevx.10.011070] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/15/2023]
Abstract
We consider cumulative merging percolation (CMP), a long-range percolation process describing the iterative merging of clusters in networks, depending on their mass and mutual distance. For a specific class of CMP processes, which represents a generalization of degree-ordered percolation, we derive a scaling solution on uncorrelated complex networks, unveiling the existence of diverse mechanisms leading to the formation of a percolating cluster. The scaling solution accurately reproduces universal properties of the transition. This finding is used to infer the critical properties of the susceptible-infected-susceptible model for epidemics in infinite and finite power-law distributed networks. Here, discrepancies between analytical approaches and numerical results regarding the finite-size scaling of the epidemic threshold are a crucial open issue in the literature. We find that the scaling exponent assumes a nontrivial value during a long preasymptotic regime. We calculate this value, finding good agreement with numerical evidence. We also show that the crossover to the true asymptotic regime occurs for sizes much beyond currently feasible simulations. Our findings allow us to rationalize and reconcile all previously published results (both analytical and numerical), thus ending a long-standing debate. Complex networks represent the interaction pattern for many real-world phenomena such as epidemic spreading. The simplest and most fundamental model for the diffusion of infectious diseases without acquired immunity predicts a vanishing epidemic threshold in the limit of large systems. In other words, no matter how small the infectiousness of the disease, there is always a finite fraction of the overall population which is infected for long times. So far, the detailed mechanism underlying this phenomenology has remained unclear. Here, we provide a complete and quantitative understanding of the model’s behavior. While the role of hubs (individuals with high connectivity) was already believed to be important, we fully clarify its nature, pointing out the highly nontrivial interplay among hubs. Each hub acts as an infection hotbed and the global epidemic emerges from hubs reinfecting each other. Surprisingly, this mechanism is at work even when the hubs are not in direct mutual contact but transmit the infection through chains of low-connectivity individuals. The survival of the epidemic is then a manifestation of a novel, long-range, percolation process among distant hubs, whose properties explain the behavior of the epidemic model. These findings rationalize and reconcile previously published results and point out long-range indirect interactions as potentially crucial ingredients for other collective phenomena in networked systems.
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