Controlling the Spread of an Epidemic in Agriculture: The Case of Xylella fastidiosa

The etiological agent of olive trees disease known as olive quick decline syndrome (OQDS) is the plant pathogenic bacterium Xylella fastidiosa, which is a vector borne bacterium. The main vector of Xylella fastidiosa in Southern Italy has been identified in the so-called meadow spittlebug, i.e., the Philaenus spumarius, a xylem sap-feeding specialist. Their juvenile form (nymphs) develops on weeds or ornamental plants, confined in a foam produced by themselves for protection from predators and temperature, while their adult forms move to olive tree canopies. Once a plant is infected, bacteria multiply within the xylem vessels inducing the production of a gel in the plant xylem, which occludes the xylem vessels, thus inhibiting the flux of water through the lymph vessels eventually blocking the nutrition of the plant. Typical symptoms are leaf scorch, dieback of twigs, branches, and even of the whole plant (Carlucci et al., Phytopathol Mediterr., 52, 541–544). Sanitation of infected olive trees is unfeasible. The aim of this chapter is to present results obtained by the authors of this monograph in a series of recent papers. The three steps are (i) mathematical modelling of the population dynamics of the ecosystem in the presence of the infection, (ii) possible strategies for the eventual eradication of the disease, (iii) computational experiments supporting the theoretical outcomes.