Epidemics on plants: Modeling long-range dispersal on spatially embedded networks

Area of Science:

• Plant pathology
• Epidemiology
• Mathematical modeling

Background:

• Classical compartmental models like SIS and SIR do not fully capture plant epidemic complexities.
• Real plant epidemics are influenced by spatial factors and long-range pathogen dispersal.

Purpose of the Study:

• To develop a generalized epidemic model for plant populations.
• To incorporate spatial characteristics and long-range dispersal into plant epidemic modeling.

Main Methods:

• Developed a novel epidemic model generalizing SIS and SIR models.
• Utilized random rectangular graphs to represent spatial characteristics of fields.
• Employed Mellin and Laplace transforms for modeling long-range pathogen dispersal.

Main Results:

• Long-range dispersal significantly favors pathogen propagation.
• Field elongation increases the epidemic threshold and reduces the number of infected plants.
• The model reproduces observed patchy infection zones and lack of clear propagation fronts.

Conclusions:

• The developed model provides a more realistic framework for understanding plant epidemics.
• Spatial structure and dispersal mechanisms are critical determinants of plant disease spread.
• The findings offer insights into managing plant diseases in agricultural and natural settings.