Mathematical models represent essential tools allowing a quantitative analysis of an epidemic system with the consequent identification of possible strategies to control a disease outbreak or even to prevent it. However, to be used in decision-making, they must be carefully parametrized and validated with epidemiological data as well as biological information on the relevant players. Here, benefitting of the Olive Quick Decline Syndrome (OQDS) outbreak, which has occurred in Southern Italy since 2013, an epidemiological model describing this epidemic is presented. Beside the bacterium Xylella fastidiosa, the OQDS main players considered in the model are its insect vectors, Philaenus spumarius, and the host plants (olive trees and weeds) of the insects and of the bacterium. The model is based on a system of ordinary differential equations, the analysis of which have provided interesting results about possible equilibria of the epidemic system and guidelines for its numerical simulations. These, under a variety of parameter scenarios, have led to the model sensitivity analysis, hence to understanding the parameters relative importance in the transmission of the disease. Although the model presented here is mathematically rather simplified, its analysis has highlighted threshold parameters that could be the target of control strategies within the integrated pest management framework, not requiring the removal of the productive resource represented by the olive trees. Indeed numerical simulations support the outcomes of the mathematical analysis according to which a removal of a suitable amount of weeds biomass (reservoir of Xylella fastidiosa) from olive orchards and surrounding areas resulted the most efficient strategy to control the spread of the OQDS. In addition, as expected, the adoption of more resistant olive tree cultivars has been shown to be a good strategy, though less cost-effective, in controlling the pathogen.