Geodesic
Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology
J. B. Burie1 ; A. Calonnec2 ; A. Ducrot1
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
Mathematical modelling of natural phenomena, Tome 1 (2006) no. 1, pp. 49-62

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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.
DOI : 10.1051/mmnp:2006003

J. B. Burie 1 ; A. Calonnec 2 ; A. Ducrot 1

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 
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J. B. Burie; A. Calonnec; A. Ducrot. Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology. Mathematical modelling of natural phenomena, Tome 1 (2006) no. 1, pp. 49-62. doi: 10.1051/mmnp:2006003

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