A Comparative Analysis of Different Fractional Optimal Control Strategies to Eradicate Bayoud Disease in Date Palm Trees

Bayoud disease, caused by Fusarium oxysporum f. sp. albedinis, is a major threat to date palm trees. It leads to lower crop yields, financial losses, and decreased biodiversity. The complexity of the disease presents challenges to effective disease management. This study introduces a mathematical model comprising six compartments for palm trees: susceptible trees, resistant varieties, exposed trees, infected trees, isolated trees under treatment, and recovered trees, along with a contaminant water compartment. The model emphasizes the role of resistant varieties, contamination of irrigation water, and the treatment of infected trees in disease control. Theoretical analyses guarantee positivity, boundedness, and the existence of a unique solution. The existence of equilibrium points (disease-free and endemic) and the reproduction number (R0) of the model are calculated analytically and validated through numerical simulations. Stability analysis at disease-free and endemic equilibrium points is conducted in terms of R0. Sensitivity analysis identifies key parameters influencing disease dynamics and is helpful to identify the potential control parameters. An optimal control problem is formulated to minimize infection spread and associated costs via preventive isolation and treatments, irrigation water treatment, and the promotion of resistant varieties. Numerical simulations demonstrate the efficacy of these strategies, highlighting the potential of resistant varieties and treatment measures in reducing infection rates and enhancing tree health. This research offers valuable insights into sustainable Bayoud disease management, underscoring the importance of mathematical modeling in addressing agricultural challenges.