Effect of External Wastage and Illegal Harvesting on the Fishery Model of the Halda River Ecosystem in Bangladesh

The Halda, a 98-kilometre long major tributary of Karnaphuli River in the Chattogram Hill Tracts, is the only source of naturally fertilized eggs of carp fishes in South Asia and a great contributor to Bangladesh fisheries sector. Waste from large factories, Hathazari Peaking Power Plant and a housing estate are polluting the water body of Halda river to such an extent that the indigenous sweetwater brood fishes are facing death and the quantity of their release of carp spawn is decreasing. The present paper examines a predatorprey fishery system by taking into account the toxin waste which can lead to polluted system. Both fish species obey the logistic population growth with their respective environmental carrying capacities. The equilibria existed in the model are investigated together with the local and global stability. Bifurcation diagrams are studied to examine the dynamical behaviors of the system. Bionomic equilibria, optimal harvesting policy and Optimal Control Theory are applied to reduce the external toxic substance. Finally, a numerical simulation of the model has been discussed to illustrate the effect of toxicity and their control upon both the predator and the prey species.