A Bioeconomic Prey-Predator Model with a Water-Pollution Modification Parameter and Stability Analysis

Abstract

Managing interacting fish populations requires consideration of ecological processes and human pressures across reserve and unreserved zones. This study developed and analyzed a bioeconomic predator–prey model for three interacting fish populations: cichlids, tilapia, and Nile perch. The model incorporated water pollution, harvesting, migration, and predation across both zones. Equilibrium points and their existence conditions were derived, and the local stability of selected equilibria was assessed using Jacobian linearization and the Routh–Hurwitz criterion. Numerical simulations examined the effects of pollution control, predation control, and a combined strategy integrating water-quality improvement and migration. The results indicated that stronger pollution control enhanced fish population persistence in the unreserved zone. The combined strategy produced greater improvements than individual interventions, while predator–prey interactions remained integral to the modeled ecosystem. These findings highlight the potential benefits of coordinating water-quality improvement and migration management to support fish population persistence. The model provides an analytical framework for evaluating management strategies that account for pollution, harvesting, and ecological interactions in aquatic systems with reserve and unreserved zones.