Terry Alan J
Division of Mathematics, University of Dundee, Dundee, Scotland, UK.
J Math Biol. 2010 Dec;61(6):843-75. doi: 10.1007/s00285-009-0325-0. Epub 2010 Jan 20.
We consider a model for a creature inhabiting two patches between which migration may occur. The creature is assumed to have a life cycle with two stages, namely juvenile and adult, giving rise to a delay differential system. The creature could represent an insect crop pest whilst the patches could represent neighbouring farms. Given that it is common to control crop pests by adult impulsive culling, we impose an adult impulsive culling regime on each patch. We find conditions on the regimes such that the pest will be eradicated on both patches simultaneously. The regime on one patch is assumed to be independent of the regime on the other patch to reflect the possibility that the patches represent farms with different owners where each owner has autonomy in their pest control decisions. In the special case where the birth functions on both patches are of an Allee type, we calculate explicit finite upper bounds for the number of culls needed on each patch to guarantee eradication. Simulations corroborate our theoretical results.
我们考虑一个关于栖息在两个斑块之间且可能发生迁移的生物的模型。假设该生物具有一个包含两个阶段（即幼年和成年）的生命周期，由此产生一个时滞微分系统。该生物可以代表一种昆虫农作物害虫，而斑块可以代表相邻的农场。鉴于通过成年期脉冲捕杀来控制农作物害虫很常见，我们在每个斑块上施加成年期脉冲捕杀机制。我们找到了这些机制的条件，使得害虫能在两个斑块上同时被根除。假设一个斑块上的机制与另一个斑块上的机制相互独立，以反映斑块代表不同所有者的农场，且每个所有者在其害虫控制决策上具有自主权这种可能性。在两个斑块上的出生函数均为阿利效应类型的特殊情况下，我们计算出每个斑块上为保证根除所需捕杀次数的明确有限上界。模拟结果证实了我们的理论结果。
