Prevention and control of OQDS (olive quick decline syndrome) outbreaks caused by Xylella fastidiosa

In Southern Italy, since 2013, there has been an ongoing Olive Quick Decline Syndrome (OQDS) outbreak, due to the bacterium Xylella fastidiosa, which has caused a dramatic impact from both socio-economic and environmental points of view. The main players involved in OQDS are represented by the insect vector, Philaenus spumarius, its host plants (olive trees and weeds) and the bacterium, X. fastidiosa. 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 (most of these olive trees were monumental ones) and on the economy. Based on a mathematical model expressed in terms of a nontrivial system of ordinary differential equations, our analysis has provided a clear picture of all possible steady states (feasible equilibria) and their stability properties, corresponding to a variety of different parameter scenarios; all of this has been illustrated by a set of computational experiments. A significant original contribution of this paper is the proof of the global asymptotic stability of each of the feasible equilibria under its existence assumptions, a fact that excludes multiple equilibria under the given conditions. It has emerged that the removal of a suitable amount of weed biomass (host plants of the juvenile stages of the insect vector of X. fastidiosa) from olive orchards and surrounding areas leads to the eradication of the epidemic, without requiring neither the removal nor the substitution of the existing olive trees.