Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology

被引：15
作者：
Burie, J. B. [1 ]
Calonnec, A. [2 ]
Ducrot, A. [1 ]
机构：
[1] Univ Bordeaux 2, CNRS, UMR 5466, MAB & INRIA Futurs, F-33076 Bordeaux, France
[2] UMR INRA ENITA Sante Vegetale, INRA CR Bordeaux, F-33883 Villenave Dornon, France
来源：
MATHEMATICAL MODELLING OF NATURAL PHENOMENA | 2006年 / 1卷 / 01期
关键词：
phytopathology; SIR model; travelling waves; singular perturbations;
D O I：
10.1051/mmnp:2006003
中图分类号：
Q [生物科学];
学科分类号：
07 ; 0710 ; 09 ;
摘要：
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.
引用
收藏
页码：49 / 62
页数：14
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