"Determining how to slow the spread of invasive species cost-effectively"
Invasive species are spreading worldwide, causing damage to ecosystems, biodiversity, agriculture, and human health. Efforts to prevent the establishment of invasive species in new areas sometimes fail, which necessitates the containment of established invaders to prevent or slow their spread to the rest of the country or continent. A major question is, therefore, how to cost-effectively allocate treatment efforts over space and time to contain the species’ population. However, identifying the optimal strategy for containing a species that propagates over large areas is a complex and challenging task that requires novel methodology and computational techniques. I will present a model with an integral-differential equation characterizing the spatial dynamics of the invasive species, incorporating the response of the species to some treatment. I will then present a novel algorithm, which finds (a) the optimal allocation of treatment efforts over space and (b) the optimal target speed at which the species should be allowed to propagate. The results show that, when using the optimal treatment, the annual cost of treatment could be tens or hundreds of percentages lower than that of some other treatments that result in the same propagation speed. It also reveals when it is cost-effective to abandon the species, when to slow or stop its spread, and when to reverse the species’ propagation and slowly eradicate it. In particular, I will 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.