Analysis of A Predator-Prey Model with The Effects of Threshold Harvesting

¹ Department of Mathematics, Faculty of Mathematics and Natural Sciences, Papua University, 98312 Manokwari, Indonesia
² Department of Agriculture, Faculty of Agriculture, Papua University, 98312 Manokwari, Indonesia

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Abstract

This study develops and analyzes a predator-prey model within an extended Lotka-Volterra framework that incorporates a Holling Type II functional response and a threshold-based harvesting strategy. Two ecological regimes were considered: a non-harvesting regime, where population densities remain below prescribed thresholds, and a harvesting regime activated once these thresholds are exceeded. The analysis begins with the identification of equilibrium points, followed by a local stability analysis using the Jacobian matrix and eigenvalue criteria. In the absence of harvesting, three biologically meaningful equilibria are obtained: trivial, semitrivial, and interior equilibria representing prey-predator coexistence. The stability of these equilibria depends on key biological parameters, such as predator mortality and prey intraspecific competition. When threshold harvesting is introduced, the interior equilibrium can be stabilized if the harvesting thresholds are chosen appropriately. Numerical simulations confirm that threshold-based harvesting may stabilize dynamics that are unstable in the non-harvesting case, although this effect is highly sensitive to harvesting parameters and exploitation intensity. The results highlight the importance of well-designed threshold harvesting policies for sustainable ecosystem management and long-term prey-predator coexistence.