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

页码：49 / 62

页数：14

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