A mathematical model of flavescence dorée epidemiology

Flavescence dorée (FD) is a disease of grapevine transmitted by an insect vector, Scaphoideus titanus Ball. At present, no prophylaxis exists, so mandatory control procedures (e.g. removal of infected plants, and insecticidal sprays to avoid transmission) are in place in Italy and other European countries. We propose a model of the epidemiology of FD by taking into account the dierent aspects involved into the transmission process (acquisition of the disease, latency and expression of symptoms, recovery rate, removal and replacement of infected plants, insecticidal treatments, and the eect of hotbeds). The model was constructed as a system of rst order nonlinear ODEs in four compartment variables. A bifurcation analysis shows that, in the absence of hotbeds, the state of healthy vineyard is stable, if removal and replacement of infected plants is implemented. In the presence of hotbeds, depending on the grapevine density, we nd either a single family of equilibria in which the health of the vineyard gradually deteriorates for progressively more severe hotbeds, or multiple equilibria that give rise to sudden transitions from a nearly healthy vineyard to a highly deteriorated one when the severity of the hotbeds crosses a critical value. These results show the long-term risks in planting new vineyards in environmental situations where strong hotbeds of FD are present or may arise in the surroundings.