Math. Model. Nat. Phenom.
Volume 5, Number 6, 2010Ecology (Part 2)
|22 - 37
|08 April 2010
Modelling the Spread of Infectious Diseases in Complex Metapopulations
Departament d’Informàtica i Matemàtica Aplicada Universitat de
* E-mail: email@example.com
Two main approaches have been considered for modelling the dynamics of the SIS model on complex metapopulations, i.e, networks of populations connected by migratory flows whose configurations are described in terms of the connectivity distribution of nodes (patches) and the conditional probabilities of connections among classes of nodes sharing the same degree. In the first approach migration and transmission/recovery process alternate sequentially, and, in the second one, both processes occur simultaneously. Here we follow the second approach and give a necessary and sufficient condition for the instability of the disease-free equilibrium in generic networks under the assumption of limited (or frequency-dependent) transmission. Moreover, for uncorrelated networks and under the assumption of non-limited (or density-dependent) transmission, we give a bounding interval for the dominant eigenvalue of the Jacobian matrix of the model equations around the disease-free equilibrium. Finally, for this latter case, we study numerically the prevalence of the infection across the metapopulation as a function of the patch connectivity.
Mathematics Subject Classification: 92D30 / 92D40
Key words: metapopulations / infectious diseases / reaction-diffusion processes
© EDP Sciences, 2010
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.