Continuous traveling waves for prey-taxis

Spatially moving predators are often considered for biological control of invasive species. The question arises as to whether introduced predators are able to stop an advancing pest or foreign population. In recent studies of reaction-diffusion models, it has been shown that the prey invasion can only be stopped if the prey dynamics observes an Allee effect. In this paper, we include prey-taxis into the model. Prey-taxis describe the active movement of predators to regions of high prey density. This effect leads to the observation that predators are drawn away from the leading edge of a prey invasion where its density is low. This leads to counterintuitive result that prey-taxis can actually reduce the likelihood of effective biocontrol.