# Fitting a lattice model with local and global transmission to spread of a plant disease

## TL;DR

This paper uses a new mathematical model to study how a citrus disease spreads locally, showing it works well with real data.

## Contribution

The paper applies a lattice-based model for the first time to a specific plant disease system, emphasizing local transmission.

## Key findings

- The lattice model fits experimental data on Bahia bark scaling well, showing significant local infections.
- The model estimates epidemiological parameters similar to those from a dispersal-kernel model.
- The lattice approach can predict disease spread and aid in optimizing control strategies.

## Abstract

Understanding, predicting and managing the spread of plant pathogens is crucial given the economic, societal and climatic benefits of plants, including crops and trees. Mathematical models have long been used to investigate disease dynamics in plants. An important component of such models is to account for spatial structure, since plant hosts are immobile and a majority of disease spread will often be localised. Here we apply a lattice-based mathematical modelling approach, a pair approximation, to model disease spread. While this method has previously been used to develop epidemiological theory, it has not been used to predict spread in a specific pathosystem. We fit our lattice-based epidemiological model to experimental data relating to Bahia bark scaling of citrus, an economically-important disease in north-eastern Brazil, and compare its performance to a more commonly used dispersal-kernel modelling approach. We show that the lattice-based model fits the data well, predicting a significant degree of near-neighbour infections, with similar estimated values of epidemiologically-meaningful parameters to the dispersal model. We highlight the pros and cons of the lattice-based approach and discuss how it may be used to predict disease spread and optimise control of plant diseases.

Plant diseases can have significant impacts, including reducing crop yields, limiting the availability of natural spaces, and the knock-on effects on our wellbeing. Mathematical models have long been used to understand how disease spreads through plant populations. Here we apply a form of mathematical model that has not previously been specifically applied to a real disease system that emphasises neighbour-to-neighbour spread of infection. In particular, we use the model to explore the spread of Bahia bark scaling of citrus, for which we have excellent experimental data available of its spatial spread. We show that the model fits the data best when there is significant neighbour-to-neighbour spread with very rare long-range infections. We show that this approach agrees well with a more commonly-used mathematical framework and highlight how it might be used to test disease management strategies.