Optimal Resource Allocation for Controlling Invasive Species

The introduction of invasive alien species is recognised as an important cause of the drastic loss of biodiversity that is affecting our planet, due to the alteration of ecosystems caused by the rapid proliferation of alien species. Invasive species cost billions of dollars a year in ecological damage and economic losses. The reduction or elimination of those alien species that threaten ecosystems, habitats or native species is a strategic objective to be carefully pursued with knowledge-based management practices. Given the extent of the problems caused by invasive species and the limited resources available to control them, planning processes are required to identify cost-effective solutions that minimize the negative impacts of invasive species on colonized systems. Careful planning requires a high capacity for analyzing the extent of the invasion and an equally high capacity for predicting its evolution in time and space. Starting from the results in [1] and [2], in [3] we develop a model capable to mimic the relevant features of the alien species invasion as well as the results of a control action when the species dynamics is influenced by external driving forces. We propose a parabolic optimal control model for both predicting the spread of the species and designing a strategy for the optimal spatiotemporal allocation of resources necessary to perform a control action, under a budget constraint. We show the analytical and numerical aspects of this approach.