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Modelling the Spread of Infectious Diseases in ComplexMetapopulations

Published online by Cambridge University Press:  08 April 2010

J. Saldaña
J. Saldaña*
Affiliation:
Departament d’Informàtica i Matemàtica Aplicada Universitat de Girona, 17071 Girona Catalonia, Spain
*
*E-mail: joan.saldana@udg.edu
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Abstract

Two main approaches have been considered for modelling the dynamics of the SIS model oncomplex metapopulations, i.e, networks of populations connected by migratory flows whoseconfigurations are described in terms of the connectivity distribution of nodes (patches)and the conditional probabilities of connections among classes of nodes sharing the samedegree. In the first approach migration and transmission/recovery process alternatesequentially, and, in the second one, both processes occur simultaneously. Here we followthe second approach and give a necessary and sufficient condition for the instability ofthe disease-free equilibrium in generic networks under the assumption of limited (orfrequency-dependent) transmission. Moreover, for uncorrelated networks and under theassumption of non-limited (or density-dependent) transmission, we give a bounding intervalfor the dominant eigenvalue of the Jacobian matrix of the model equations around thedisease-free equilibrium. Finally, for this latter case, we study numerically theprevalence of the infection across the metapopulation as a function of the patchconnectivity.

Keywords

metapopulationsinfectious diseasesreaction-diffusion processes
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 6: Ecology (Part 2) , 2010 , pp. 22 - 37
Copyright
© EDP Sciences, 2010

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