Optimal controls and cost-effectiveness analysis on the transmission dynamics of early blight disease in tomatoes

This study investigates the transmission dynamics of early blight disease in tomatoes using optimal control theory and cost-effectiveness analysis. A nonlinear ordinary differential equation (ODE) model is formulated to evaluate integrated control strategies, including shading, mulching, and fungicide application, aimed at reducing infections while accounting for implementation costs. The disease-free and endemic equilibria are analyzed, and the effective reproduction number R_e is derived using the next-generation method. The influence of model parameters on disease transmission was evaluated using local sensitivity analysis based on the Normalized Forward Sensitivity Index (NFSI) and global sensitivity analysis via Latin Hypercube Sampling coupled with Partial Rank Correlation Coefficients (PRCC). Time-dependent control strategies are incorporated, and the necessary optimality conditions are derived using Pontryagin's Maximum Principle. Numerical simulations, performed using the Runge-Kutta method, show that the combined implementation of shading, mulching, and fungicide application substantially reduces the infected plant population. However, incremental cost-effectiveness analysis (ICEA) indicates that mulching alone is the most cost-effective individual strategy, providing significant disease reduction at a relatively low implementation cost, whereas the combined strategy achieves greater disease suppression but at higher cost.