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All Journal Zero : Jurnal Sains, Matematika, dan Terapan
Askal, Oky
Department of Mathematics, Universitas Syiah Kuala, Aceh, Indonesia
Agriculture, Biological Sciences & Forestry Chemistry Mathematics Physics

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Routh-Hurwitz Stability Analysis of the Predator-Prey Model with Prey Population Harvesting in Polluted Aquatic Ecosystems Fiska, Nissa; Ikhwan, Muhammad; Nurmaulidar, Nurmaulidar; Askal, Oky
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 2 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i2.26061

Abstract

Environmental pollution and overharvesting are critical external factors that disrupt predator–prey balance in aquatic ecosystems. This study develops a two-dimensional nonlinear predator–prey model incorporating both toxicity and harvesting. Local stability is analyzed using the Routh–Hurwitz criterion, and findings are validated through numerical simulations under varied initial conditions. The system yields four equilibria: E0, E1 and E1 are unstable extinction states, while the interior equilibrium E*= (0.4146, 1.0899) is locally stable, with Tr(J)=-1.3052 and det(J)=0.4177. Stability is preserved as long as the combined toxicity–harvesting parameter remains below approximately 4.1-4.2 day-1. The novelty of this work lies in explicitly quantifying threshold effects of harvesting and toxicity, showing that coexistence is achievable under moderate external pressures. These results highlight that sustainable management requires keeping exploitation and pollution below critical thresholds to ensure long-term persistence of both prey and predator.
Co-Authors Fiska, Nissa Muhammad Ikhwan Nurmaulidar, Nurmaulidar