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
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.