Open AccessA Proposed Bio-Economic Model for the Prey-Predator Fishery Model with Harvesting: Toward Modeling Dynamics in Applied Mathematics
Author(s) -
Moayad H. Ismaeel,
Azhar Abbas Majeed
Publication year - 2019
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1362/1/012142
Subject(s) - cichlid , predation , population , equilibrium point , lyapunov function , nile tilapia , predator , mathematics , overexploitation , fishery , ecology , mathematical economics , biology , fish <actinopterygii> , nonlinear system , oreochromis , physics , differential equation , mathematical analysis , demography , quantum mechanics , sociology
This study proposed and analyzed a mathematical model. The proposed model was used for studying the two-prey predator system dynamics in relation to the fishery model. One of the parameters that were considered involved the possible impact of harvesting on the target populations. In particular, ecological dynamics were studied relative to tilapia, cichlid, and the Nile perch as pre-predator systems. Through system non-dimensionalization, the study computed equilibrium points before obtaining the conditions for global and local instability. To achieve the local instability condition, the investigation used Routh-Hurwitz Criterion and eigenvalues approach. With appropriate Lyapunov function defined, the coexistence equilibrium was proved. In turn, there was the analysis of the bio-economic equilibrium before conducting numerical simulations to verify the analytical outcomes that the study obtained. From the numerical results, the study established that if tilapia and cichlid fishes are not overharvested, the three species are likely to coexist. The populations were observed to play a crucial role to the Nile perch population’s growth rate. Hence, the study’s proposed mathematical model proved informative in such a way that it paved the way for the fishery control management departments to avoid overharvesting tilapia and cichlid fishes.