Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks

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...

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Autores principales:	Claudio Castellano, Romualdo Pastor-Satorras
Formato:	article
Lenguaje:	EN
Publicado:	American Physical Society 2020
Materias:	Physics QC1-999
Acceso en línea:	https://doaj.org/article/8b38898f821b465986e9fb294ba26742
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spelling	oai:doaj.org-article:8b38898f821b465986e9fb294ba267422021-12-02T11:38:36ZCumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks10.1103/PhysRevX.10.0110702160-3308https://doaj.org/article/8b38898f821b465986e9fb294ba267422020-03-01T00:00:00Zhttp://doi.org/10.1103/PhysRevX.10.011070http://doi.org/10.1103/PhysRevX.10.011070https://doaj.org/toc/2160-3308We 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.Claudio CastellanoRomualdo Pastor-SatorrasAmerican Physical SocietyarticlePhysicsQC1-999ENPhysical Review X, Vol 10, Iss 1, p 011070 (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Physics QC1-999
spellingShingle	Physics QC1-999 Claudio Castellano Romualdo Pastor-Satorras Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks
description	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.
format	article
author	Claudio Castellano Romualdo Pastor-Satorras
author_facet	Claudio Castellano Romualdo Pastor-Satorras
author_sort	Claudio Castellano
title	Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks
title_short	Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks
title_full	Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks
title_fullStr	Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks
title_full_unstemmed	Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks
title_sort	cumulative merging percolation and the epidemic transition of the susceptible-infected-susceptible model in networks
publisher	American Physical Society
publishDate	2020
url	https://doaj.org/article/8b38898f821b465986e9fb294ba26742
work_keys_str_mv	AT claudiocastellano cumulativemergingpercolationandtheepidemictransitionofthesusceptibleinfectedsusceptiblemodelinnetworks AT romualdopastorsatorras cumulativemergingpercolationandtheepidemictransitionofthesusceptibleinfectedsusceptiblemodelinnetworks
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Cumulative Merging Percolation and the Epidemic Transition of the Susceptible-Infected-Susceptible Model in Networks

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