Modeling of the Invasion of a Fungal Disease over a Vineyard

Jean-Baptiste Burie,1 Agnes Calonnec,2 and Michel Langlais1

1 UMR CNRS 5466, Mathematiques Appliquees de Bordeaux, INRIA futurs, Equipe Anubis, case 26, Universite Victor Segalen Bordeaux 2,146 rue Leo Saignat, 33076 Bordeaux Cedex, France; [email protected]

2 INRA-CR de Bordeaux, UMR INRA-ENITA en Sante v^getale, BP 81, 33883 Villenave d'Ornon, France; [email protected]

Summary. The spatiotemporal spreading of a fungal disease over a vineyard is investigated using a susceptible-exposed-infected-removed (SEIR)-type model coupled with a set of partial differential equations describing the dispersal of the spores. The model takes into account both short and long range dispersal of spores and growth of the foliar surface. Results of numerical simulations are presented. A mathematical result for the asymptotic behavior of the solutions is given as well.

Key words: SEIR model, dispersal, diffusion, large time behavior.

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