A Mathematical Model For Coffee Berry Borer Management In Coffee Farm With Optimal Control

Abstract

The Coffee berry borer (CBB) is the most destructive pest that affects the productivity of Coffee worldwide. The female CBB drills the coffee berry eat the seed and reproduce inside it. This study investigated the infestation dynamics of CBB and its optimal management. For this, we formulated and analyzed a mathematical model describing the progression of CBB. The proposed model includes; Coffee berry biomass, Coffee berry borer population and awarded farmers’. First, we analyzed the dynamical properties of the governing model including the boundedness of the solution, existence of borer free and endemic equilibrium, local and global stability of equilibrium points. The basic reproduction number R0 was calculated using the next-generation matrix and the stability of the equilibrium points were analyzed. From the qualitative analysis, the borer free equilibrium point is both locally and globally stable if R0 < 1, and the endemic equilibrium point is also both locally and globally stable if R0 > 1. Furthermore, sensitivity analysis of the model equation was performed on the key parameters to find out their relative significance and potential impact on the infesta tion dynamic of CBB. Then we extend the proposed model into an optimal control problem. The optimal control strategy is found by minimizing the number of coffee borer (pest) indi vidual with taking into account the cost of implementation. The existence of optimal controls is proved with the help of Pontryagin’s Minimum Principle. Then, numerical simulations of the model equations were carried out using MATLAB. Finally, the numerical simulations show that the agreement with the analytical results.