Optimal control of spatial-dynamic processes: The case of biological invasions

This study examines the spatial nature of optimal bioinvasion control. We develop and parameterize a spatially explicit two-dimensional model of species spread that allows for differential control across space and time, and we solve for optimal control strategies. We find that the qualitative nature of optimal strategies depend in interesting ways on aspects of landscape and invasion geometry. For example, we show that reducing the extent of exposed invasion edge, through spread, removal, or strategically employing landscape features, can be an optimal strategy because it reduces long-term containment costs. We also show that optimal invasion control is spatially and temporally “forward-looking” in the sense that strategies should be targeted to slow the spread of an invasion in the direction of greatest potential long-term damages. These and other novel findings contribute to the largely nonspatial literature on optimally controlling invasions and to understanding control of spatial-dynamic processes in general.