Environmental model to manage the eradication of almond trees of Alicante (Spain) in the case of Xylella fastidiosa

Mathematical-computational modelling is a very valuable tool for decision-making and proper management of the protocols used to
limit the damage caused by an epidemic in living beings. Biological invasions are a process with four stages: arrival, establishment,
spread and concentration. All the processes involved can model on a system of ordinary differential equations (ODE) that describes the evolution of populations confined in compartments according to their states. However, this type of modelling has some shortcomings, for example, not considering local interactions between the individuals that make up the population. In addition, differential equations assume that individuals are homogeneously distributed, and all connected to each other, therefore, it is difficult to access the individual dynamics that can occur. These difficulties can be overcome by discrete models (based on agents or cellular automata).
Our compartmental model bases on a time-space representation in the form of a grid in which each cell represents either a tree that can be infected under the influence of the whole ecosystem. The state of the grid is updated over time. As many grids as factors in the entire ecosystem will be considered. The update rules and the definition of the probabilities of infection will be described by Boolean rules and neighbourhood environments in the grids.
Our proposal provides suitable modelling to the spread of plant pest and particularly to the propagation of Xf in the almond trees. This approach allows the study of the response of the individual trees according to both the combination of variables of an ecosystem and their intensity. Another advantage of the model is that it allows easy scaling when the number of characteristics of the ecosystem increases. These encouraging results can guide the modeling of tools to  advise the appropriate control.