Controlling the Spread of an Epidemic in Agriculture—the Case of Xylella Fastidiosa: A Research Project

In this paper, an extension is reported of the spatially structured mathematical model for a Xylella fastidiosa epidemic, presented in previous papers by the same authors, concerning the dynamics of a predator, i.e. Zelus renardii, which has been recently suggested as a possible biocontrol agent of the X. fastidiosa insect vector Philaenus spumarius. By taking into account previous investigations, the choice of the functional response to predation is indeed crucial; this significantly depends upon the role of the predator with respect to the insect vector of the epidemic. Possible choices adopted in literature are the Holling type II for a specialist predator, and the Holling type III for a generalist predator. The analysis reported here shows that a specialist predator, whenever identified, would indeed lead to the eventual eradication of a Xylella epidemic. Unfortunately our investigations have shown that the adoption of the generalist predator Z. renardii is not an efficient control strategy to eradicate a Xylella epidemic. For the time being, weed cut and/or selected cultivar have been confirmed as effective control measures. We sketch future research directions, mainly concerning the role of seasonality with respect to possible control interventions.