Pervasive Threats and Optimal Control of Lantana Camara Invasion in an Ecosystem

Abstract Lantana camara is a highly invasive plant species that poses serious ecological threats to native vegetation and herbivores in savanna ecosystems. This study develops and analyzes a mathematical model to understand the competitive dynamics between L. camara , native vegetation, and herbivores. The model incorporates interspecific competition, herbivory, and logistic growth, and it is extended to include three targeted control strategies: mechanical uprooting, biological control via insect introduction, and enhancement of competitive native species. Analytical results reveal conditions for species extinction and persistence, while sensitivity analysis identifies key parameters influencing the herbivore survival threshold. An optimal control problem is formulated and solved using Pontryagin’s Maximum Principle and numerical simulations. Results indicate that individual controls can reduce L. camara impact, but an integrated approach yields the most ecologically beneficial outcomes, supporting native vegetation recovery and herbivore persistence. These findings offer a quantitative basis for designing effective, multi-pronged strategies to manage invasive species in complex ecosystems.