How to combine multiple tactics over time and space to optimize the treatment of harmful invasive species

Harmful invasive species are spreading worldwide, causing severe damage to biodiversity, agriculture, human health, and infrastructure. Virtually all developing countries attempt to manage and suppress invasions, which includes surveillance and eradication of newly detected populations, and containment to slow the spread of larger, established populations of invasive species. However, attempts to eradicate and contain invasive species often fail due to the lack of well-designed strategies dictating when and where to apply each of the various treatment tactics and technologies. In my talk, I will demonstrate how to use optimal control theory to determine the optimal, most cost-effective strategy to manage invasive species in two study systems. In the first study, we ask how to optimally combine three treatment tactics: pesticide application, mating disruption, and sterile male release. We show that each of the three tactics is most efficient across a specific range of population densities. Furthermore, we show that mating disruption and sterile male release inhibit the efficiency of each other, and therefore, they should not be used simultaneously. However, since each tactic is effective at different population densities, different combinations of tactics should be applied sequentially through time when a multiple-annum eradication program is needed. In the second study, we ask how to stop the spread of a propagating front of an invasive species while minimizing the annual cost of treatment. We show that the optimal strategy often comprises eradication in the yet-uninvaded area, and under certain conditions, it also comprises maintaining a “suppression zone” - an area between the invaded and the uninvaded areas, where treatment reduces the invading population but without eliminating it. We examine how the optimal strategy depends on the demographic characteristics of the species and reveal general criteria for deciding when a suppression zone is cost-effective.