Optimal control of invasive species through a dynamical systems approach

Abstract

Effectively dealing with invasive species is a pervasive problem in environmental management. The damages that stem from invasive species are well known. However, controlling them cost-effectively is an ongoing challenge, and mathematical modeling and optimization are becoming increasingly popular as a tool to assist management. In this paper we investigate problems where optimal control theory has been implemented. We show that transforming these problems from state–costate systems to state-control systems provides the complete qualitative description of the optimal solution and leads to its theoretical expression for free terminal time problems. We apply these techniques to two case studies: one of feral cats in Australia, where we use logistic growth; and the other of wild-boars in Italy, where we include an Allee effect.