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We investigate the structure of travelling waves for a model of a fungal disease propa- gating 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.

Singular Perturbation Analysis of Travelling Waves for a Model in Phytopathology