1. Spectral properties of the connectivity matrix and the SIS-epidemic threshold for mid-size metapopulations
- Author
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David Juher, Víctor Mañosa, Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions, and Ministerio de Ciencia e Innovación (Espanya)
- Subjects
Accurate estimation ,Grafs, Teoria de ,Applied Mathematics ,Spectral properties ,Epidemics -- Mathematical models ,Complex networks ,Metapopulation ,Complex network ,Instability ,Anàlisi de xarxes (Planificació) ,Uncorrelated ,Informàtica::Informàtica teòrica::Algorísmica i teoria de la complexitat [Àrees temàtiques de la UPC] ,Graph theory ,Modeling and Simulation ,Epidèmies -- Models matemàtics ,Matemàtiques i estadística::Probabilitat [Àrees temàtiques de la UPC] ,SIS epidemic ,Statistical physics ,60 Probability theory and stochastic processes::60J Markov processes [Classificació AMS] ,37 Dynamical systems and ergodic theory::37N Applications [Classificació AMS] ,05 Combinatorics::05C Graph theory [Classificació AMS] ,Mathematical economics ,Mathematics ,Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs [Àrees temàtiques de la UPC] - 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).
- Published
- 2021