Math. Model. Nat. Phenom.
Volume 9, Number 2, 2014Epidemics models on networks
|Page(s)||108 - 120|
|Published online||24 April 2014|
Spectral Properties of the Connectivity Matrix and the SIS-epidemic Threshold for Mid-size Metapopulations
1 Dept. Informàtica, Matemàtica
Aplicada i Estadística, Universitat de Girona, 17071, Girona, Spain
2 Dept. Matemàtica Aplicada III, Universitat Politècnica de Catalunya, 08222, Terrassa, Spain
Corresponding author. E-mail: firstname.lastname@example.org
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.
Mathematics Subject Classification: 05C82 / 60J28 / 37N25
Key words: SIS epidemic / complex networks
© EDP Sciences, 2014
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