Powdery mildew (Erysiphe necator , Vitis vinifera ) is a disease caused by a fungus. It has been imported from the United States in the mid -nineteenth century. Though it does not kill its host, it is the cause of the destruction of vine grapes.

This disease is mainly treated preventively with many fungicide applications throughout the growing period of the vine. These treatments have a relatively low economic cost , but they are harmful to the environment and human health.

The primary contamination is due to spores that survived winter. These spores , once deposited on the young leaves in April germinate and create colonies of mycelium. The secondary contaminations are caused by spores produced on the surface of the mycelium. Until autumn, the disease has several secondary cycles of germination, mycelium growth, spore production and dispersion by wind.

Many factors influence the development of the disease , which could explain the high spatio- temporal variability in the severity of powdery mildew epidemics . These factors interact with each other are linked to climate (temperature, wind speed and direction, humidity) , host (architecture, leaf age ... ) , the conduct of the vine ( variety used, rows of vines, pruning ... ) and pathogenic ( initial contamination).

To better understand the interactions between host growth and development of the disease, we have proposed several models: a mechanistic mode at the vine scale, a model based on differential equations at the vine scale and finally a partial differential equation model type reaction-diffusion at the plot scale.

These models allow to gain insight for the best times to conduct fungicide treatment depending on the condition of the vine. They also allow to study the influence on the progression of the epidemic with different spatial distributions combining different stocks vigors or varietal mixtures .

epidemiology; plant pathology; reaction-diffusion equations