Mitigating Black Pod Disease in Cocoa Plants: An Optimal Control and Cost‐Effectiveness Analysis

Black pod disease (BPD), caused by Phytophthora species, continues to pose a significant threat to cocoa production, particularly in tropical regions where cocoa farming is a major economic activity. This study develops a deterministic compartmental model to understand the transmission dynamics of BPD and evaluate the impact of multiple control strategies. The model incorporates key compartments representing susceptible, infected, removed, and treated cocoa pods, and accounts for cultural practices, chemical treatment, and rouging as time‐dependent control variables. We analyze the basic reproduction number and disease‐free equilibrium, and apply Pontryagin's Maximum Principle to derive necessary conditions for optimal control. Numerical simulations are conducted to evaluate the effectiveness of various combinations of control strategies. Our results show that combining cultural practices and rouging yields the most cost‐effective reduction in disease burden. The study offers valuable insights into the timing and intensity of interventions necessary to manage BPD effectively.