Hypersensitive Optimal Control of Invasive Species

Effectively dealing with invasive species is a pervasive problem in environmental management. The damages, and associated costs, that stem from invasive species are well known, as is the benefit from their removal. We investigate problems where optimal control theory has been implemented, and we show that these problems can easily become hypersensitive, making their numerical solutions unstable. We show that transforming these problems from state-adjoint systems to state-control systems can provide useful insights into the system dynamics and simplify the numerics. 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. A further development is to optimize the control strategy by taking into account the spatio-temporal features of the invasive species control problems over large and irregular environments. The approach is used in a management scenario where the invasive species to be controlled with an optimal allocation of resources is the deciduous tree Ailanthus Altissima, infesting the Alta Murgia National Park in the south of Italy. This work has been carried out within the H2020 project ECOPOTENTIAL (http://www.ecopotential-project.eu), coordinated by CNR-IGG. The project has received funding from the European Union's Horizon 2020 research and innovation programme (grant agreement No 641762).