Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology

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

Mathematical Modelling of Natural Phenomena (2010)

  • Volume: 1, Issue: 1, page 49-62
  • ISSN: 0973-5348

Abstract

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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.

How to cite

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Burie, J. B., Calonnec, A., and Ducrot, A.. "Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology." Mathematical Modelling of Natural Phenomena 1.1 (2010): 49-62. <http://eudml.org/doc/222363>.

@article{Burie2010,
abstract = { 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. },
author = {Burie, J. B., Calonnec, A., Ducrot, A.},
journal = {Mathematical Modelling of Natural Phenomena},
keywords = {phytopathology; SIR model; travelling waves; singular perturbations},
language = {eng},
month = {3},
number = {1},
pages = {49-62},
publisher = {EDP Sciences},
title = {Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology},
url = {http://eudml.org/doc/222363},
volume = {1},
year = {2010},
}

TY - JOUR
AU - Burie, J. B.
AU - Calonnec, A.
AU - Ducrot, A.
TI - Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology
JO - Mathematical Modelling of Natural Phenomena
DA - 2010/3//
PB - EDP Sciences
VL - 1
IS - 1
SP - 49
EP - 62
AB - 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.
LA - eng
KW - phytopathology; SIR model; travelling waves; singular perturbations
UR - http://eudml.org/doc/222363
ER -

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