Section: New Results

Modeling in viticulture

This is a collaborative research with INRA Villenave d'Ornon (UMR Santé Végétale).

Spreading of a fungal disease over a vineyard

Participants : Jean-Baptiste Burie, Michel Langlais, Arnaud Ducrot.

This is a joint work with A. Calonnec. Using a suitable re-formulation in the form of a nonlinear integral equation with measure kernel convolutions, we were able to prove existence of travelling fronts for the previous models we considered in [7] . In particular, this framework applies to reaction-diffusion systems coupled with ordinary differential equations with or without time delay. It also applies to integro-differential system of equations. This allows to prove the existence of travelling fronts for more general models of disease propagation than the ones considered so far: the spores dispersal is not necessarly modelized by Fickian diffusion [26] .

In the framework of M. Charron's Master degree internship, the code used for simulations in [7] has been improved by using a more efficient discretization method and it now also handles spatial heterogeneity. It has been used to compare the results of the mathematical model with those of the mechanistic model and with field data. This work will be the subject of a future publication.

With Pierrick Legrand (EPI Alea, Bordeaux Sud ouest), using Matlab we started to build a user-friendly front end to the code used for the simulations at the vineyard scale. It allows to easily define spatial heterogeneities for the vinestock vigors and test various cases of primary infections.

Prediction of insect dynamics over a vineyard

Participants : Ahmed Noussair, Bedr'Eddine Ainseba, Jacques Henry, Delphine Picart.

This research is done in collaboration with D. Thiery (INRA Villenave d'Ornon). The goal is to promote and coordinate research on integrated control strategies in viticulture which reduce inputs of pesticides. This collaboration ended in february with the defense of Delphine Picart PhD thesis.