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Spectral Properties of the Connectivity Matrix and the SIS-epidemic Threshold for Mid-size Metapopulations

Published online by Cambridge University Press:  24 April 2014

D. Juher  and
V. Mañosa
D. Juher*
Affiliation:
Dept. Informàtica, Matemàtica Aplicada i Estadística, Universitat de Girona, 17071, Girona, Spain
V. Mañosa
Affiliation:
Dept. Matemàtica Aplicada III, Universitat Politècnica de Catalunya, 08222, Terrassa, Spain
*
⋆ Corresponding author. E-mail: david.juher@udg.edu
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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.

Keywords

SIS epidemiccomplex networks
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 2: Epidemics models on networks , 2014 , pp. 108 - 120
Copyright
© EDP Sciences, 2014

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