Application of the diffusion equation for modelling splash dispersal of point-source pathogens

Area of Science:

• Plant Pathology
• Mathematical Modeling
• Agricultural Science

Background:

• Splash dispersal is a key mechanism for pathogen spread in agriculture.
• Colletotrichum acutatum causes strawberry anthracnose, impacting crop yield.
• Understanding pathogen dispersal is crucial for disease management.

Purpose of the Study:

• To develop and parameterize a mathematical model for splash dispersal of point-source pathogens.
• To investigate the influence of ground cover and rain intensity on dispersal patterns.
• To assess the applicability of the diffusion equation for modeling splash dispersal.

Main Methods:

• Developed a splash dispersal model based on probability density functions of random displacement vectors.
• Parameterized the model using experimental data for Colletotrichum acutatum.
• Tested the model across three ground covers (plastic, soil, straw) and two rain intensities (15 and 30 mm h⁻¹).

Main Results:

• The developed model is the fundamental solution of the classic diffusion equation.
• Model parameters showed good fit for different ground covers and rain intensities, with R² values from 0.80 to 0.96.
• The diffusion equation effectively models splash dispersal from a point source over homogeneous ground cover.

Conclusions:

• The diffusion equation provides a promising framework for modeling splash dispersal of plant pathogens.
• The model's accuracy across varied conditions highlights its potential for disease management strategies.
• Further research can refine the model for complex environments and diverse pathogens.