Mathematical model and optimal control analysis of coffee berry borer with temperature and rainfall variability

Abstract

This study focuses on a nonlinear deterministic mathematical model for coffee berry borer (Hypothenemus hampei) with temperature and rainfall variability. In the model analysis, CBB free and coexistence equilibria are computed. The basic reproduction numbers at a minimum and maximum temperature and rainfall are derived. The qualitative analysis of the model revealed the scenario for equilibria together with basic reproduction numbers. The local stability of equilibria is established through the Jacobian matrix and the Routh–Hurwitz criteria, while the global stability of equilibria is demonstrated using an appropriate Lyapunov function. The normalized sensitivity analysis has also been performed to observe the impact of different parameters on basic reproduction numbers. The proposed model is extended into an optimal control problem by incorporating two control variables, namely, the preventive measure variable based on the separation of susceptible coffee berries from contacting the pests based on biological control and an increase in the death rate of colonizing females of CBB based on chemical control. Optimal disease control analysis is examined using Pontryagin’s minimum principle. Finally, the numerical simulations are performed based on analytical results and are discussed quantitatively. Furthermore, the cost-effectiveness of control strategies to determine the best approach to minimize the CBB burden was studied. The study is significant in providing reliable information on how one can use mathematical modeling to improve the roles of control strategies and prevention in CBB transmission in a coffee farm. The outcome of the study may guide public agriculture policymakers on optimal control strategies to control the pests. In particular, using chemical pesticides is very effective to combat pests with minimum costs.