Mathematical Modeling and Optimal Control of Cocoa Black Pod Disease in Osun State, Nigeria

Abstract

Aims: Cocoa black pod disease poses a significant threat to global cocoa production, affecting both yield and quality. This article presents a comprehensive study on the modeling and optimal control of cocoa black pod disease. Place and Duration of Study: Data for this study was collected from Cocoa farms in Osun State, Nigeria and those available in the literature. Methodology: Using the stability theory of differential equations, the study developed a mathematical model that describe the dynamics of black pod disease transmission! in relation to the stage at which cocoa pods are developing as well as the disease’s transmission pathways and its control mechanism, the study also explores the application of optimal control strategies to mitigate the impact of the disease on cocoa crops. The study calculated the basic reproduction number for cocoa black pod disease (CBPD) using the next generation matrix method. The prerequisites for CBPD-free and endemic equilibria’s local and global stability are established. Sensitivity analysis in the study indicates that R0 is most sensitive to the rates of diseased pods removal, fungicide application, and healthy pods harvesting. To optimally control the disease, Pontryagin’s Maximum Principle(PMP) was applied to determine the best strategy to optimally control the disease. Results: Numerical simulations suggested that either of Strategy 3 or 4 are best suitable for effective disease control. Conclusion: The proposed optimal control measures provide a foundation for the design of targeted interventions, aiding cocoa farmers, researchers, and policymakers in safeguarding global cocoa production against this detrimental disease. This research contributes to the ongoing efforts to ensure the resilience and sustainability of the cocoa industry in the face of emerging challenges.