Routh-Hurwitz Stability Analysis of the Predator-Prey Model with Prey Population Harvesting in Polluted Aquatic Ecosystems

Nissa Fiska, Muhammad Ikhwan, Nurmaulidar Nurmaulidar, Oky Askal

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.

Keywords


Enviromental management; Equilibrium points; Population interaction; Steady state; Toxicity.

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DOI: http://dx.doi.org/10.30829/zero.v9i2.26061

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