Extinction Criteria in Stage-Structured Population Models with Impulsive Culling

We propose stage-structured population models for species whose adult members are subject to culling, with a view to understanding the culling regimes that are likely to result in eradication of the species. A purely time-dependent model is proposed in which culling occurs at particular discrete times, not necessarily equally spaced. Then a reaction-diffusion model is proposed for a situation in which the adults can diffuse; in this model the culling is continuous in time but occurs only at particular discrete points in space. Such a model might be appropriate for pheromone trapping of insects. For both models conditions are obtained that are sufficient for species eradication.