Section: New Results

Invasion processes and modeling in epidemiology

Participants : Jean-Baptiste Burie, Arnaud Ducrot.

We have derived a homogenized version of our model of a fungal of disease of vine(see [7] ) that takes into account the periodic row structure of vineyards. We used two-scale homogenization of Nguentseng and Allaire (see e.g. [20] ): the macroscopic scale is the vineyard scale while the microscopic one is the plant scale. We have proved a result of convergence towards the homogenized model and numerical simulations have demonstrated a significant gain in computing time and stability.

These results have been presented at ECMTB2011 in Krakow (and also, at the Exploratory Workshop on Emerging Infectious Diseases and Mathematical Modelling, Barcelona 2011 and seminars at Franche-Comté University, Tamkang and National Taiwan University).

An article is to be submitted in SIAM J. Multiscale Modeling and Simulation in early 2012.