THE IMPACT OF POLLUTION REDUCTION ON THE DYNAMICS AND OPTIMAL HARVESTING OF A PLANKTON-FISH SYSTEM IN A POLLUTED ENVIRONMENT

Abstract

In this work, we study a three-species plankton-fish system in a polluted environment with linear harvesting and pollution reduction efforts. We considered a deterministic model consisting of a system of three nonlinear differential equations. We investigated the existence, uniqueness, and boundedness of solutions, followed by the dynamical behaviour near steady states. This is done using the Jacobian matrix and the Lyapunov function. Finally, we presented an optimal harvest problem with the help of the Pontryagin Maximum Principle. Numerical simulations are performed to demonstrate the significant outcomes of the study using MATLAB 2013 a software.