Threshold-Driven Integrated Management of the Coffee Berry Borer: Insights from Bifurcation Analysis

The coffee berry borer (Hypothenemus hampei) is the primary pest of coffee crops worldwide. Sustainable management strategies increasingly rely on the integration of biological control and interventions activated by population thresholds. In this work, a comparative framework based on dynamical systems is presented, integrating three complementary mathematical models to analyze different management strategies for the coffee berry borer. First, a biologically structured three-dimensional model describes the interaction between adult and immature borers and predatory ants. Second, a two-dimensional formulation allows the maximum per capita consumption rate of the predator to be studied as a bifurcation parameter, identifying critical parameter values that delimit regions of coexistence or effective pest control. Finally, a piecewise-smooth dynamical system incorporates ethological control activated when infestation exceeds a predefined threshold, whose effectiveness depends on the capture intensity associated with the traps. Using stability theory, bifurcation analysis, and techniques from piecewise-smooth dynamical systems, parametric regions associated with persistence, coexistence, or significant pest reduction are characterized. The results show that biological control alone may be insufficient if a predation threshold is not exceeded, whereas its combination with early threshold-based interventions considerably enlarges the dynamical regions favorable to producers. This study provides a dynamical interpretation of the agricultural concept of intervention threshold and offers a quantitative framework to strengthen integrated management and the sustainability of coffee production.