Optimal control and cost-effectiveness analysis of coffee berries invasion with Hypothenemus hampei dynamics

Abstract

This study emphases on a nonlinear deterministic mathematical model for the invasion dynamics of Hypothenemus hampei. To gain an insight into the global dynamics of coffee berry borer transmission and eradication in any given coffee farm, the assumption of logistic growth with carrying capacity is to reflect the fact that the amount of coffee plants depends on the limited size of the coffee farm available. Equilibria are computed and basic reproduction number was derived. The local and global stability of equilibria are established through the Routh Hurwitz-criteria and Lyapunov function, respectively. The proposed model is extended into an optimal control problem by incorporating preventive measure, an increase in the death rate of colonizing and infesting females of borer. Finally, the numerical simulations are performed based on analytical results. The finding of this study shows that the use of a combination of cultural practices and traps is very effective in combating pests with minimum costs.