Program
| MSG5c | |
|---|---|
| Jean-Baptiste Burie | |
| Institut Mathematiques de Bordeaux, Universite Victor Segalen Bordeaux2, France | |
| Title | Modelling of a powdery mildew epidemic over a vineyard |
| Abstract | In this talk, we consider several models for the propagation of a plant pathogen over a canopy. We focus on a fungal epidemic of powdery mildew over a vineyard. The vector of contamination is the spores that stem from the lesions at the surface of the leaves. We introduce a model at the vinestock scale. It is a variant of a SEIR model and is based on a system of five ODEs. We use data from a mechanistic model to identify the parameters of our model and perfom a sensitivity analysis. One of the specific features of this epidemic that will be discussed is that the host growth cannot be neglected during the development of the disease, and moreover, the leaves cannot be infected once they become too old (ontogenic resistance). Next we investigate the propagation of the epidemy at the vineyard scale. So the previous model is extended by adding two PDEs to describe the short (intra-cep) and long (inter-cep) range dispersal of the spores. The spatial structure of the vineyard is periodic. Again we study the influence of the parameters of the model and of the periodic spatial structure on the epidemic. Eventually we give a result on the existence and unicity of travelling wave solutions, that is solutions of the form U(x-ct) where x is the 1D space variable, t is time and c the constant wave speed, for a variant of the previous spatial model. The proof uses a re-formulation in the form of an integral equation with measure kernel convolutions. As we are concerned with the long term behavior of the solutions, in this part of the talk we do not take into account the host growth. |
| Location | Woodward 5 |