A Conservative Nonlocal Framework for Airborne Fungal Epidemics in Fruit Crops

Abstract

Purpose: Airborne fungal epidemics in fruit crops combine local infection processes with finite-distance inoculum movement; splash-dispersed diseases are considered only as candidate extensions. We developed a conservative nonlocal framework that distinguishes local infection intensity from spatial epidemic footprint and can accommodate polycyclic fruit–pathogen systems after pathogen-specific extension and calibration. Methods: Susceptible, latent, and sporulating host tissue were coupled to a nonlocal equation for free inoculum. We establish sufficient conditions for global well-posedness, positivity, and boundedness and derive a spatial next-generation threshold. A synthetic Botrytis cinerea case study used unclipped second-order strong stability-preserving Runge–Kutta [SSPRK(2,2)] simulations to compare local diffusion and nonlocal kernels with moment-matched controls, numerical refinement, periodic and absorbing boundaries, and targeted sensitivity analyses. Results: Numerical undershoots remained at roundoff scale. On the 200-m grid, the 5-m Gaussian increased infected-tissue-equivalent length from 30.74 to 33.70 m relative to local diffusion, whereas the original mixed kernel increased it to 88.63 m. With mean and variance matched, changing tail shape increased equivalent length to 39.16 m; an 8-m directional shift increased it to 61.56 m. On a 600-m absorbing domain, broad and directional kernels retained larger footprints than local baselines, although their ranking changed. Conclusions: Dispersal scale, tail shape, and directional displacement have distinct effects on epidemic footprint and influence spatial-extent metrics more strongly than peak local infection. The framework is a candidate structure for other fruit diseases, but each application requires pathogen-specific states, forcing, observation models, calibration, and validation.