Modelling and analysis of temperature and rainfall variability impact on the coffee berry borer infestation with optimal control

Abstract

This study focuses on a nonlinear deterministic mathematical model for the impact of temperature and rainfall variability on coffee berry borer \emph{(Hypothenemus hampei)}. 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 colonising 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 finding of this study shows that the use of chemical pesticides is very effective to combat pests with minimum costs.