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Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations

We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovery and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks

Supported by Ministry of Economy and Competitiveness of the Spanish Government grant numbers MTM2011-27739-C04-03 (first author) and DPI2011-25822 (second author). Also by Generalitat de Catalunya projects 2009-SGR-345 (first author) and 2009-SGR-1228 (second author).

info:eu-repo/grantAgreement/MICINN//MTM2011-27739-C04-03/ES/MODELIZACION MATEMATICA, BIOLOGIA TEORICA Y REDES COMPLEJAS/

EDP Sciences

Manager: Ministerio de Ciencia e Innovación (Espanya)
Author: Juher, David
Mañosa, V.
Date: 2014 January 1
Abstract: We consider the spread of an infectious disease on a heterogeneous metapopulation defined by any (correlated or uncorrelated) network. The infection evolves under transmission, recovery and migration mechanisms. We study some spectral properties of a connectivity matrix arising from the continuous-time equations of the model. In particular we show that the classical sufficient condition of instability for the disease-free equilibrium, well known for the particular case of uncorrelated networks, works also for the general case. We give also an alternative condition that yields a more accurate estimation of the epidemic threshold for correlated (either assortative or dissortative) networks
Supported by Ministry of Economy and Competitiveness of the Spanish Government grant numbers MTM2011-27739-C04-03 (first author) and DPI2011-25822 (second author). Also by Generalitat de Catalunya projects 2009-SGR-345 (first author) and 2009-SGR-1228 (second author).
Format: application/pdf
Document access: http://hdl.handle.net/10256/13736
Language: eng
Publisher: EDP Sciences
Collection: info:eu-repo/semantics/altIdentifier/doi/10.1051/mmnp/20149207
info:eu-repo/semantics/altIdentifier/issn/0973-5348
info:eu-repo/semantics/altIdentifier/eissn/1760-6101
Is part of: info:eu-repo/grantAgreement/MICINN//MTM2011-27739-C04-03/ES/MODELIZACION MATEMATICA, BIOLOGIA TEORICA Y REDES COMPLEJAS/
Rights: Tots els drets reservats
Subject: Epidèmies -- Models matemàtics
Epidemics -- Mathematical models
Title: Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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