Coffee is the most critical stimulant beverage in the world and represents a significant source of income in many tropical and subtropical countries. In this paper, a deterministic mathematical model has been formulated to describe the infestation dynamic of coffee berry borer (CBB) using a system of non-linear ordinary differential equations with farmers' awareness and optimal control. The system has two equilibrium points, namely the CBB free equilibrium point and the endemic equilibrium point which exist conditionally. The basic reproduction number, which plays a vital role in mathematical epidemiology, was derived. The qualitative analysis of the model revealed the scenario for both CBB free equilibrium and endemic equilibrium points. The local stability of the equilibria is established via the Jacobian matrix and Routh–Hurwitz criteria, while the global stability of the equilibria is proven by using an appropriate Lyapunov function. The normalized sensitivity analysis has also been performed to observe the impact of different parameters on the basic reproduction number. We extended the proposed model into an optimal control problem by incorporating two control variables, the effort made to reduce the colonizing females based on chemicals, traps, and biological control using entomopathogenic fungi such as Beauveria bassiana, that are applied to the surface of the coffee berries and kill the colonizing females of CBB when they drill an entry hole into the coffee berry and the effort made to increase the awareness of farmers through media campaign and education for the coffee farmer. Then the optimal control strategy is found by minimizing the number of CBB individuals considering the cost of implementation. The existence of optimal controls is examined using Pontryagin's minimum principle. Finally, the numerical simulations show agreement with the analytical results.

咖啡是世界上最重要的提神饮料，也是许多热带和亚热带国家重要的收入来源。在本文中，使用具有农民意识和最优控制的非线性常微分方程系统，制定了确定性数学模型来描述咖啡浆果蛀虫 (CBB) 的侵染动态。系统有两个平衡点，即CBB自由平衡点和有条件存在的地方性平衡点。推导了在数学流行病学中起着至关重要作用的基本再生数。模型的定性分析揭示了 CBB 自由平衡点和地方病平衡点的情景。平衡的局部稳定性是通过雅可比矩阵和 Routh-Hurwitz 准则建立的，而平衡的全局稳定性通过使用适当的 Lyapunov 函数证明。还进行了归一化敏感性分析，以观察不同参数对基本再生数的影响。我们通过合并两个控制变量将所提出的模型扩展为最优控制问题，基于化学品、陷阱和生物控制使用昆虫病原真菌（如Beauveria bassiana应用于咖啡浆果表面，当 CBB 雌性在咖啡浆果上钻一个入口孔时会杀死它们，并通过媒体宣传和对咖啡农的教育来提高农民的意识。然后在考虑实施成本的情况下，通过最小化 CBB 个体的数量来找到最优控制策略。使用 Pontryagin 的最小原则检查是否存在最优控制。最后，数值模拟与分析结果一致。