Dynamical Mathematical Behavior and Influence of Nutrients, Dissolved Oxygen on Survival of Fish Population

Abstract

A new mathematical model is proposed to study the effects of increasing nutrients and algae with decreasing dissolved oxygen on survival of fish population. The equations are modelled by considering four interacting variables (concentration of nutrients, density of algal population, concentration of dissolved oxygen and fish population) using Hollings type II interaction. It is assumed that the nutrients are constantly release into the waterbodies from various sources (agricultural runoffs, domestic sewage, industrial effluents etc.), due to which the algae grow abundantly depleting the dissolved oxygen. Unfortunately, the marine life is facing the adverse effects of this. In this view, the mathematical model is formulated and the equilibrium points of the model are obtained to study the dynamical mathematical behavior of the system. The stability of equilibrium points is studied and analyzed in detail using the Routh-Hurwitz criteria.  Lastly, the numerical simulation is performed to illustrate the analytical findings of the proposed model.