Speaker
Description
Olive Quick Decline Syndrome (OQDS), caused by the bacterium Xylella fastidiosa, is a vector-borne disease affecting olive groves across Europe, severely impacting areas of southern Italy. We consider an ODE model for the olive tree canopies, the vector insects, and the weeds. Under the assumption that the insects reproduce significantly faster than the trees and weeds, the model equations are singularly perturbed and can then be analysed via the dynamical systems-based geometric singular perturbation theory. This allows us to reduce the long term dynamics of the model solutions to the dynamics of a globally attracting slow manifold. We extend the model by introducing a Heaviside cut-off to the spread of the disease cross terms and regularise by applying the desingularisation technique, know as "blow-up".
