咖啡是全球经济中的重要农产品,由于咖啡豆的数量和质量受到咖啡浆果的严重影响,hopthenemushambei(法拉利),CBB,它的主要害虫。对付这种甲虫的方法之一是通过生物防治剂,像蚂蚁(膜翅目:Formicidae),其中一些的特点是自然居住在咖啡种植园,并在其所有生命阶段以CBB为食。我们的论文通过基于常微分方程的新颖数学模型考虑了这两种昆虫之间的捕食者-食饵相互作用,其中状态变量对应于成人CBB,不成熟的CBB,来自一个物种的蚂蚁,没有说明捕食CBB是否是他们的喂养习惯之一,在成年和未成熟阶段。通过这个新的数学模型,我们可以定性地预测系统中存在的不同动力学,因为一些有意义的参数是变化的,填补了文献中现有的空白,并设想了害虫的管理方法。数学上,确定了系统的平衡点,并通过定性理论对其稳定性进行了研究。应用分岔理论和数值模拟来说明结果的稳定性。被解释为物种共存的条件,以及根除害虫的条件,至少在理论上,通过生物防治作用与其他集中于仅消除成年CBB的作用相结合。
Coffee is a relevant agricultural product in the global economy, with the amount and quality of the bean being seriously affected by the coffee berry borer Hypothenemus hampei (Ferrari), CBB, its principal pest. One of the ways to deal with this beetle is through biological control agents, like ants (Hymenoptera: Formicidae), some of which are characterized by naturally inhabiting coffee plantations and feeding on CBB in all their life stages. Our paper considers a predator-prey interaction between these two insects through a novel mathematical model based on ordinary differential equations, where the state variables correspond to adult CBBs, immature CBBs, and ants from one species, without specifying whether preying on the CBB is among their feeding habits, in both adult and immature stages. Through this new mathematical model, we could qualitatively predict the different dynamics present in the system as some meaningful parameters were varied, filling the existing gap in the literature and envisioning ways to manage pests. Mathematically, the system\'s equilibrium points were determined, and its stability was studied through qualitative theory. Bifurcation theory and numerical simulations were applied to illustrate the stability of the results, which were interpreted as conditions of the coexistence of the species, as well as conditions for eradicating the pest, at least theoretically, through biocontrol action in combination with other actions focused on eliminating only adult CBBs.