A field scale model for the spread of fungal diseases in crops: the example of a powdery mildew epidemic over a large vineyard

Abstract

The aim of this article is to derive an asymptotic two‐scale model for the propagation of a fungal disease over a large vineyard. The original model is based on a singularly perturbed system of two linear reaction‐diffusion equations coupled with a set of nonlinear ordinary differential equations in a highly heterogeneous medium. We prove the well‐posedness of the asymptotic model and obtain a convergence result confirmed by numerical simulations. Copyright © 2014 John Wiley & Sons, Ltd.