K.O. Muka

Itebukunmi is a riverine community in Ondo State Nigeria, known for its high traffic in fishing activities. The economic importance of fishing activities in Itebukunmi to the Nigerian economy necessitate the need to study the harvesting strategy of fishing in Itebukunmi waters and where necessary determine scientifically regulatory policy that will ensure sustained growth in population.
The Mathematical model of three species of fishes in Itebukunmi couple with human activites was derived using systems of ordinary differential equations. The qualitative analysis of the model such as the local, global, stability and bioeconomic analysis were done using linearization approach and bifurcation analysis. The result of the quantitative analysis showed that : as the control of the harvesting rate of cat fish increases, the population of cat fish and African knife fish, in Itebukunmi river increases, while the Ophiocephalus fish population decreases. Also, as the control of the harvesting rate of Ophiocephalus fish increases, the population of Ophiocephalus fish and African knife fish, in Itebukunmi river increases, while the cat fish population decreases. Furthermore, as the control of the harvesting rate of African knife fish increases, the population of African knife fish , in
Itebukunmi river increases, while the cat fish and Ophiocephalus fish population decreases