A new spatial model for tracking plant spore dispersal and disease spread

Abstract

Plant diseases caused by spores can cause severe damage to crop production, resulting in yield losses of up to 75%. Spores can be carried over long distances by wind, water, insects, and humans, meaning that even one infected agricultural field can spread the disease to neighboring fields. Although mathematical models exist to describe the spread of plant diseases, they often do not take into account the transport and location of spores, which limits the ability to make spatial forecasts. To address this limitation, we developed a spatial model based on Healthy sites H, Latent sites L, Infected sites I, Removed sites R, and spore sites X (HLIRX), which describes the spore movement between fields, allowing us to simulate the spatial invasion of plant diseases. We analyzed the existence and stability of steady states in the model using the finite difference method. Our findings reveal that the disease-free equilibrium is unstable, while the boundary and endemic equilibria are asymptotically stable, depending on the spore dispersion term. Moreover, we observed that the dynamics of the population in each field exhibit a consistent pattern, with leftward or rightward shifts depending on the distance from the source of infection, which cannot be captured from the temporal model. We also investigated the impact of two spatial parameters, the dispersal kernel parameter and spore migration rate, and found that both parameters lead to an increase in the number of infected plants but have no significant effect on disease severity. In addition, we discovered that the time until the infected population peaks is linearly related to the distance between each field and the source of infection, with a Pearson correlation coefficient greater than 0.99 (p < 0.001). Our developed model provides a useful tool for studying the spatial dispersion of plant diseases distributed by spores, as it considers the transport and location of spores and can be used to make spatial forecasts.