Predators as a possible strategy for controlling a {\it Xylella} epidemic?

In Southern Italy, since 2013, there has been an  ongoing Olive Quick Decline Syndrome (OQDS) outbreak, due to the bacterium {\it Xylella fastidiosa},     which has caused a dramatic impact  from  both socio-economic and environmental  points of view.     Current agronomic practices are mainly based on uprooting the sick olive trees and their surrounding ones,     with later installment of olive cultivars more resistant to the bacterium infection.     Unfortunately, both of these practices are having an undesirable impact on the environment and on the economy. Here, a spatially structured mathematical model has been  proposed   to include  a  predator  {\it Zelus renardii } as a possible biocontrol agent of the  {\it Xylella} epidemic.  The  fact  that {\it Z. renardii} has been reported to be a generalist   predator implies that its   introduction  is not an efficient control  strategy   to eradicate a {\it Xylella} epidemic. Instead,  a specialist predator, whenever identified, would  lead to the eventual eradication  of a {\it Xylella} epidemic.   In   either  cases it has   been confirmed that a significant reduction of the  weed biomass  can lead to  the eradication of the vector  population,  hence of a  {\it Xylella} epidemic, independently of the presence of predators.