利用最优控制导航蜂巢螨虫侵扰的微妙几何结构
Navigating the Delicate Geometry of Beehive Mite Infestation with Optimal Control
浏览论文内容
中文总结 AI 辅助
本文通过含阿利效应的动力系统模型与最优控制，揭示杀螨剂剂量权衡，提出“冲击与维持”策略，并预测螨害将促使蜂群向小型抗性演化。
中文摘要 AI 辅助
寄生螨虫瓦螨（Varroa destructor）对全球西方蜜蜂（Apis mellifera）种群构成严重的生存威胁。本文提出了一个蜂巢-螨虫相互作用的动力系统模型，该模型融入了真社会性阿利效应，以评估化学干预措施的有效性。我们将处理方式分为“温和”杀螨剂（针对外寄生螨虫）和“强烈”杀螨剂（穿透封盖巢房以靶向繁殖期螨虫）。我们的分岔分析揭示了一个基本权衡：虽然强烈处理通过移动跨临界分岔边界有效根除了受保护的螨虫库，但它们对蜜蜂施加了亚致死毒性。我们解析地证明，超过临界剂量阈值会导致灾难性的鞍结分岔，从而保证蜂群崩溃。为了规避这一毒性极限，我们利用庞特里亚金最大值原理构建了一个最优控制问题。数值解表明，一种动态的“冲击与维持”联合用药策略能在根除螨虫库与维持蜂巢活力之间取得最优平衡。将模型扩展到包含抗药性菌株表明，依赖单一化学药剂迫使蜂巢陷入高毒性、几乎不可持续的化学药物依赖循环。最后，我们的数学框架得出了一个引人注目的生态学预测：由于根除边界与蜂群的承载能力密切相关，不受控制的螨虫压力可能会施加进化力量，选择体型更小、天然具有抗性的蜂巢，而非商业农业所青睐的大型蜂群。
英文摘要
The parasitic mite Varroa destructor poses a severe existential threat to global honey bee Apis mellifera populations. In this paper, we present a dynamical systems model of hive-mite interactions incorporating a eusocial Allee effect to evaluate the efficacy of chemical interventions. We partition treatments into ``soft'' miticides (targeting phoretic mites) and ``harsh'' miticides (penetrating the capped brood to target reproductive mites). Our bifurcation analysis reveals a fundamental trade-off: while harsh treatments effectively eradicate the protected mite reservoir by shifting the transcritical bifurcation boundary, they impose sublethal toxicity on the bees. We analytically show that exceeding a critical dosage threshold culminates in a catastrophic saddle-node bifurcation that guarantees colony collapse. To navigate this toxicity limit, we formulate an optimal control problem using Pontryagin's Maximum Principle. Numerical solutions reveal that a dynamic ``shock and maintain'' cocktail strategy optimally balances reservoir clearance with hive viability. Expanding the model to include treatment-resistant strains demonstrates that single-chemical reliance forces the hive onto a highly toxic, nearly unsustainable chemical treadmill. Finally, our mathematical framework yields a striking ecological prediction: because the eradication boundary scales intimately with the colony's carrying capacity, unchecked mite pressure will likely exert evolutionary forces that select for smaller, naturally resistant hives over the massive colonies favored by commercial agriculture.
发表机构
- Florida State University（佛罗里达州立大学）
机构由 AI 辅助整理，请以论文原文为准。
