A dynamic model for a three species open-access fishery with taxation as a control instrument of harvesting efforts the case of Lake Victoria

Abstract

The Lake Victoria fishery is dominated by three commercial fish species namely Nile perch, Nile tilapia and small pelagic silver fish.The current excessive use of fishing efforts in the lake have devastating consequences to the extent of diminishing these fish species. The purpose of this study is to propose a bioeconomic mathematical model based on Lotka-Volterra dynamics by introducing taxes to the profit per unit biomass of the harvested fish of each species with the intention of controlling fishing efforts.The results of the formulated model showed that the co-existence steady state with taxation was both locally and globally assymptotically stable.The optimal harvesting policy was established using Pontryagin’s maximum principle. The numerical example illustrated that imposition of optimal taxations resulted into optimal harvesting efforts and hence optimal harvesting levels which favour the sustainability of fish species.