Geodesic
Spectral Properties of the Connectivity Matrix and the SIS-epidemic Threshold for Mid-size Metapopulations
D. Juher1 ; V. Mañosa2
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
Mathematical modelling of natural phenomena, Tome 9 (2014) no. 2, pp. 108-120.

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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.
DOI : 10.1051/mmnp/20149207

D. Juher 1 ; V. Mañosa 2

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 
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D. Juher; V. Mañosa. Spectral Properties of the Connectivity Matrix and the SIS-epidemic Threshold for Mid-size Metapopulations. Mathematical modelling of natural phenomena, Tome 9 (2014) no. 2, pp. 108-120. doi : 10.1051/mmnp/20149207. http://geodesic.mathdoc.fr/articles/10.1051/mmnp/20149207/

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