<p>Invasive alien species (IAS) pose significant threats to biodiversity, ecosystem stability, and economic sustainability, necessitating effective management strategies. This study explores the use of optimal control models to address IAS management, integrating ecological dynamics with economic considerations to design cost-efficient and ecologically sustainable interventions. We employ a combined approach, utilizing the Hamilton-Jacobi-Bellman framework and dynamic system analysis of the state-control interactions, to examine both density-independent and density-dependent control scenarios. Our analysis highlights the trade-offs between immediate control costs and long-term ecological outcomes, emphasizing the important roles of growth rates, control effectiveness, discount factors, and terminal constraints in shaping optimal strategies. Density-dependent models provide adaptive solutions that respond dynamically to population levels, while density-independent models are suited for uniform or early-stage interventions. Strong terminal constraints drive more aggressive strategies, particularly for larger populations or faster growth rates. The findings underscore the utility of this framework for policymakers, offering practical tools to design cost-effective strategies tailored to specific ecological and economic contexts. Future research could expand on this foundation by addressing spatial dynamics, budget constraints, and multi-stakeholder decision-making, further enhancing its applicability to real-world IAS management challenges.</p>