Sensitivity Analysis and Optimal Control of Cocoa Black Pod Disease Caused by Phytophora Margakarya

Abstract

To address the critical threat black pod disease poses to global cocoa production and farmer income, this study developed a novel mathematical model that utilizes a system of ordinary differential equations to capture the interactions between various stages of cocoa pods (susceptible cherelles, young/mature pods, ripe pods) and their disease state (exposed, infected). Additionally, the model incorporates the dynamics of the disease-causing pathogen population. Employing Pontryagin's Maximum Principle, the model optimizes control strategies that minimize disease impact. This optimization identifies the efficient allocation of resources, timing of interventions, and deployment of control measures like infected pod removal, fungicides, and sanitation practices. The finding of the study reveals that control measure u₃ which is rouging (pod removal) and any one of the remaining control measures is best for the treatment of cocoa black pod disease caused by Phytophora Megarkaya. These findings translate into valuable, data-driven recommendations for cocoa farmers and disease management professionals. By strategically combining infected pod removal, targeted fungicide use, and environmental management practices, farmers can significantly reduce disease severity, enhance cocoa production, and promote a more sustainable cocoa industry.