ANALYSIS OF PREY–PREDATOR MODEL WITH ALLEE EFFECT, TOXICITY AND HARVESTING

Abstract

This thesis examines a predator-prey system incorporating a strong Allee effect on the prey population, environmental pollution, and a combined strategy of harvesting and pollution reduction efforts. A modified deterministic mathematical model has been rigorously analyzed both analytically and numerically to gain deeper insights into its complex dynamics. The existence and uniqueness of solutions, as well as their boundedness and positivity, have been studied to ensure the mathematical and biological validity of the model. Particular emphasis is placed on the steady-state analysis, with a detailed investigation of the existence and stability of equilibrium points. Furthermore, the study explores optimal harvesting policies using Pontryagin’s Maximum Principle. Numerical examples are provided to illustrate key findings.