%0 Journal Article
%T Approximate aggregation of a two time scales periodic multi-strain SIS epidemic model: A patchy environment with fast migrations
%+ E.T.S. Ingenieros Industriales
%+ Departamento de Matematicas [Alcala de Henares]
%+ Institut méditerranéen d'océanologie (MIO)
%A Marva, M.
%A Bravo De La Parra, R.
%A POGGIALE, Jean-Christophe
%< avec comité de lecture
%Z MIO:12-062
%@ 1476-945X
%J Ecological Complexity
%I Elsevier
%V 10
%P 34-41
%8 2012-06
%D 2012
%R 10.1016/j.ecocom.2011.09.002
%K Nonautonomous differential equations
%K SIS model
%K Patchy model
%K Time scales
%K Approximate aggregation
%Z Mathematics [math]/Dynamical Systems [math.DS]
%Z Sciences of the Universe [physics]/Ocean, Atmosphere
%Z Environmental Sciences/Biodiversity and Ecology
%Z Environmental Sciences/Global ChangesJournal articles
%X This article is a review of spatial aggregation of variables for time continuous models. Two cases are considered. The first case corresponds to a discrete space, i.e. a set of discrete patches connected by migrations, which are assumed to be fast with respect to local interactions. The mathematical model is a set of coupled ordinary differential equations (O.D.E.). The spatial aggregation allows one to derive a global model governing the time variation of the total numbers of individuals of all patches in the long term. The second case considers a continuous space and is a set of partial differential equations (P.D.E.). In that case, we also assume that diffusion is fast in comparison with local interactions. The spatial aggregation allows us again to obtain an O.D.E. governing the total population density, which is obtained by integration all over the spatial domain, at the slow time scale. These aggregations of variables are based on time scales separation methods which have been presented largely elsewhere and we recall the main results. We illustrate the methods by examples in population dynamics and prey-predator models.
%G English
%L hal-00741586
%U https://hal.archives-ouvertes.fr/hal-00741586
%~ CNRS
%~ SDE
%~ INSMI
%~ GIP-BE
%~ MIO
%~ OSU-INSTITUT-PYTHEAS
%~ UNIV-AMU
%~ UNIV-TLN
%~ TDS-MACS
%~ TEST-AMU