Approximate aggregation of a two time scales periodic multi-strain SIS epidemic model: A patchy environment with fast migrations

Abstract : 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.
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-00741586
Contributor : Mio Aigle <>
Submitted on : Sunday, October 14, 2012 - 5:54:53 PM
Last modification on : Thursday, October 17, 2019 - 12:04:02 PM

Identifiers

Citation

M. Marva, R. Bravo de la Parra, Jean-Christophe Poggiale. Approximate aggregation of a two time scales periodic multi-strain SIS epidemic model: A patchy environment with fast migrations. Ecological Complexity, Elsevier, 2012, 10, pp.34-41. ⟨10.1016/j.ecocom.2011.09.002⟩. ⟨hal-00741586⟩

Share

Metrics

Record views

330