THE IMPACT OF POLLUTION CONTROL ON CONSERVING A POPULATION UNDER PRESSURE FROM HARVESTING AND ENVIRONMENTAL POLLUTION

Abstract

In this thesis, we study a three-dimensional deterministic model that incorporates resource biomass, pollutant stock, and harvesting effort to analyze resource dynamics. By considering effort allocation between harvesting and pollution reduction, we examine the existence, uniqueness, boundedness, and positivity of solutions for the proposed model. Additionally, we investigate the existence of nonnegative steady states and analyze their local and global stability. The findings indicate that the system admits three biologically feasible equilibrium points, each of which is locally and asymptotically stable under certain conditions. Our results highlight the effectiveness of pollution control programs in promoting resource conservation and environmental restoration. Numerical examples are provided to illustrate key outcomes, demonstrating that investing in pollution reduction not only supports resource sustainability but also enhances yield.