Optimal resource allocation for spatiotemporal control of invasive species

Controlling and planning the removal of invasive species are topics of outmost importance in management of natural resources because of the severe ecological damages and economic losses caused by non-native alien species. Optimal management strategies often rely on coupling population dynamics models with optimization procedures to achieve an effective allocation of limited resources for removing invasive species from hosting ecosystems. We analyse a parabolic optimal control model to simulate the best spatiotemporal strategy for the removal of the species when a budget constraint is applied. The model also predicts the species spread under the control action. We improve the capability of the model to reproduce realistic scenarios by introducing an advection term in the state equation. That allows to model the action of external forces, like currents or winds, which might bias dispersal in certain directions. The analytical properties of the model are discussed under suitable boundary conditions. As a further original contribution, we introduce a novel numerical procedure for approximating the solution reducing the computational costs in view of its implementation as a support decision tool. Then we test the approach by simulating the spread and the control of a hypothetical invasive plant in the territory of the Italian Sardinia island. To reproduce the anisotropy of the diffusion we include the effect of the altitude in the habitat suitability of the species.