| Issue |
Math. Model. Nat. Phenom.
Volume 1, Number 1, 2006
Population dynamics
|
|
|---|---|---|
| Page(s) | 49 - 62 | |
| DOI | https://doi.org/10.1051/mmnp:2006003 | |
| Published online | 15 May 2008 | |
Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology
1
UMR CNRS 5466, MAB & INRIA Futurs, Université
Victor Segalen Bordeaux 2, 33076 Bordeaux, France
2
INRA-CR de Bordeaux, UMR INRA-ENITA en Santé
végétale, 33883 Villenave d'Ornon
Corresponding author: ducrot@sm.u-bordeaux2.fr
We investigate the structure of travelling waves for a model of a fungal disease propagating over a vineyard. This model is based on a set of ODEs of the SIR-type coupled with two reaction-diffusion equations describing the dispersal of the spores produced by the fungus inside and over the vineyard. An estimate of the biological parameters in the model suggests to use a singular perturbation analysis. It allows us to compute the speed and the profile of the travelling waves. The analytical results are compared with numerical simulations.
Mathematics Subject Classification: 92D30 / 35K57 / 35B20 / 35B40
Key words: phytopathology / SIR model / travelling waves / singular perturbations
© EDP Sciences, 2006
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