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Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology

Published online by Cambridge University Press:  15 May 2008

J. B. Burie ,
A. Calonnec  and
A. Ducrot
J. B. Burie
Affiliation:
UMR CNRS 5466, MAB & INRIA Futurs, Université Victor Segalen Bordeaux 2, 33076 Bordeaux, France
A. Calonnec
Affiliation:
INRA-CR de Bordeaux, UMR INRA-ENITA en Santé végétale, 33883 Villenave d'Ornon
A. Ducrot*
Affiliation:
UMR CNRS 5466, MAB & INRIA Futurs, Université Victor Segalen Bordeaux 2, 33076 Bordeaux, France
*
[email protected]
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Abstract

We investigate the structure oftravelling waves for a model of a fungal disease propagating overa vineyard. This model is based on a set of ODEs of the SIR-typecoupled with two reaction-diffusion equations describing thedispersal of the spores produced by the fungus inside and over thevineyard. An estimate of the biological parameters in the modelsuggests to use a singular perturbation analysis. It allows us tocompute the speed and the profile of the travelling waves. Theanalytical results are compared with numerical simulations.

Keywords

phytopathologySIR modeltravelling wavessingular perturbations
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 1 , Issue 1: Population dynamics , 2006 , pp. 49 - 62
Copyright
© EDP Sciences, 2006

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