A model for the spread of fire blight during bloom

Abstract

We derive an infectious disease model to describe the spread of fire blight during bloom. By coupling the disease dynamics of the stationary host with the transport of the pathogen by vectors we are able to investigate the blossom blight disease cycle in a spatial setting. We use Schauder's fixed point theorem in combination with the method of upper and lower solutions to prove the existence of travelling wave solutions when the model parameters satisfy certain constraints. By studying numerical simulations we argue that it is likely that travelling waves exist for model parameters that do not satisfy these constraints. Through a sensitivity analysis we show that ooze-carrying vectors and orchard density both play a significant role in the severity of a blossom blight epidemic when compared to the growth rate of the pathogen and the mobility of ooze-carrying vectors.