On the Stability of the Interior Equilibrium Point of a Bioeconomic Model of Prey-Predator Interaction with Constant Harvesting and Reserve Zones

Abstract

A modified version of a bioeconomic model for Prey-Predator interaction in polluted environment with constant harvesting strategy and reserve zone is proposed and studied. The coexistence equilibrium state has been analysed using the method of linearization and Routh-Hurwitz criteria. The analytical results revealed that the coexistence equilibrium state is locally asymptotically stable. Results of numerical experiments carried out using Matlab R2010a agree substantially with the analytical results. The implication of the results obtained, is that creation of reserve zones have significant effects on both Tilapia and Nile perch yields in the unreserve zone. Therefore, the study recommends the creation of reserve zones with migration rate of for effective control of overexploitation and extinction of fish biomass in both reserve and unreserve zones.

Key words: Bioeconomic; Reserve Zone; Prey-Predator; Coexistence equilibrium point; Stability