Optimal Control Analysis of Rice Blast Disease with Environmental Pathogen Pool and Yield Dynamics

Abstract

The fungus Magnaporthe oryzae is the driving force behind rice blast disease, which remains a primary constraint to global rice production, often leading to yield losses exceeding 30%. This study develops and investigates a mathematical model of rice blast transmission to evaluate optimal control strategies for disease mitigation. The model partitions the rice plant population into susceptible, exposed, infectious, and removed classes, while explicitly incorporating a dynamic environmental pathogen pool and cumulative yield dynamics to account for the compounding factors that drive an outbreak. We apply Pontryagin's maximum principle to design an optimal control framework aimed at reducing infection rates of plant population and associated intervention costs. Time-dependent controls include resistant variety deployment, fungicide application, roguing of symptomatic plants, and fertilizer/irrigation enhancement. Simulation results demonstrate that fungicide application constitutes the foundational control measure, achieving approximately 84% reduction in peak infection and enabling epidemic elimination when combined with other strategies. Resistant variety deployment serves as a critical yield multiplier, transforming aggressive roguing from a catastrophically destructive practice into a highly productive integrated strategy. Furthermore, fertilizer/irrigation enhancement acts as an essential catalyst, requiring a threshold level (u4 ≥ 0.2) to convert disease suppression into realized productivity gains; without such enhancement, control investments become counterproductive. These findings indicate that optimal rice blast management requires balancing epidemiological suppression with agronomic productivity. Ultimately, the ideal strategy is contingent on whether farmers prioritize maximum yield potential or production stability, suggesting that moderate roguing rates can optimize outcomes in resistance-based integrated control systems.

DOI: https://doi.org/10.5281/zenodo.21553318