Optimal control of Cocoa Black pod disease: A multi-pronged approach

Abstract

This study presents a novel approach to controlling cocoa black pod disease, caused by Phytophthora megakarya. Unlike previous methods, we employ a mathematical modeling framework based on Pontryagin’s Maximum Principle to optimize control strategies that minimize disease impact. The model incorporates the dynamics of healthy and infected pods while considering the combined effects of three key interventions: Infected pod removal, Targeted fungicide application and Promoting a healthy growing environment. Through numerical simulations, we identify the optimal timing and intensity for each intervention to minimize infected pods over time. This study highlights the following novelties: Synergistic effect of combined control which demonstrates that combining all three strategies is significantly more effective than relying on individual methods, Optimal strategies which involves dynamically adjusting control measures throughout the growing season to adapt to disease progression, Prompt action after disease detection proves crucial for successful control. These findings offer valuable data-driven recommendations for cocoa farmers and disease management professionals. By strategically implementing a combination of infected pod removal, targeted fungicide use, and environmental management, farmers can significantly reduce disease severity, enhance cocoa production, and promote a more sustainable cocoa industry.

Keywords

• Black pod
• Cocoa
• Hamiltonian
• Optimal control theory
• Pontryagin’s maximum principle