Optimal control of invasive species with economic benefits: application to the Typha proliferation.
We address the management of invasive estuarine herbs providing some economic benefits and characterized by two modes of reproduction affecting the ecosystem. The study began by analyzing the stability of the plant dynamics using an approximate model resulting from the negligence of the seasonality in seedlings production. The optimal control seeks to find strategies with a minimal implementation cost by way of incorporating the plant profit in the payoff function. Optimal strategies were designed and implemented to control proliferation scenarios using a two-class compartmental model. Furthermore, the optimal control system was derived for the approximate model as well as for the model including the seasonality feature. Finally, numerical simulations were performed to demonstrate the effectiveness of the control laws for both systems.