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.
