Dynamics analysis of Filippov pest control model with two economic thresholds

Understanding the stages of the pest life cycle, from the juvenile class to the adult class, is crucial for developing effective pest control strategies. Targeted interventions can be tailored to each life stage, maximizing control efficiency and reducing the excessive use of pesticides; therefore, they help minimize damage to crops. With this motivation, we present a new strategy that uses the Filippov framework to describe the two stages of the pest life cycle, from the juvenile class to the adult class, with two economic thresholds. These thresholds serve as a vital signal for the timely implementation of resistance strategies. The first threshold measure is dependent on the density of juvenile pests allowed, while the second threshold is based on the density of allowed adult pests. This model assists pest control by concurrently managing both juvenile and adult populations, effectively keeping them below dangerous thresholds. By employing a dual approach to population regulation, the system ensures a comprehensive strategy for pest management. The model's dynamic behaviours, existence, and stability of various equilibria are addressed both analytically and numerically. Furthermore, we investigate sliding segment regions to determine the timing of control measures for both juvenile and adult pest populations. Additionally, we discuss the dynamics of the sliding mode, covering both local and global sliding bifurcations. The results indicate that the utilization of two economic thresholds in pest management is beneficial, as they can help prevent pest outbreaks by maintaining the density of juvenile and adult pests at desired levels.