An epidemic model to address the spread of plant pests. The case of Xylella fastidiosa in almond trees

The purpose of this paper is to present a discrete compartmental susceptible-asymptomatic-infected-dead (SAID) model to address the expansion of plant pests. The authors examined the case of Xylella fastidiosa in almond trees in the province of Alicante (Spain) to define the best eradication/contention protocol depending on the environmental parameters such as climatic factors, distance between trees, isolation of the plots, etc.

This approach considers the expansion of the disease among the almond trees orchards by means of a grid model. The cells of the grid represent a tree (or even a group of trees) that can be susceptible (healthy), asymptomatic (infected by the bacterium but without symptoms), infected or dead. When time passes, the status of the cells is determined by binary rules that update following both a neighborhood and a delay pattern. The model assumes that the environmental parameters have a crucial impact on the expansion of the disease, so a grid is assigned to each parameter to model the single effect caused by this parameter. The expansion is then the weighted sum of all the grids.

This proposal shows how the grid architecture, along with an update rule and a neighborhood pattern, is a valuable tool to model the pest expansion. This model has already been analyzed in previous works and has been compared with the corresponding continuous models solved by ordinary differential equations, coming to find the homologous parameters between both approaches. Thus, it has been possible to prove that the combination neighborhood-update rule is responsible for the rate of expansion and recovering/death of the illness. The delays (between susceptible and asymptomatic, asymptomatic and infected, infected and recovered/dead) may have a crucial impact on both the peak of infected and the recovery/death rate. This theoretical model has been successfully tested in the case of the dissemination of information through mobile social networks and is also currently under study in the case of expansion of COVID-19.

This work develops a new approach for the analysis of expansion of plant pests. This approach provides both behavioral variability at the cell level (by its capability to modify the neighborhood and/or the update rule and/or the delays) and modularity (by easy scaling the number of grids). This provides a wide range of possibilities to deal with realistic scenarios.