Dynamical Systems in Parasite-Host and Structured Population Models

研究者对生态学和种群生物学中出现的问题进行数学研究，重点是寄主-寄生虫系统和结构种群。由于它们的快速更替，寄生种群是研究进化原理的理想对象；反过来，了解这些原则对有效控制传染病也很重要。数学模型及其分析对于更深入的理解和作为设计控制和管理策略的理论实验室是非常必要的。事实上，许多关于毒力的适应性动力学的争论已经变得如此复杂，以至于用数学来表述比用语言表述更容易。虽然寄生物与宿主相互作用的健康方面是一个紧迫的问题，但它们对生物多样性的影响可能同样重要。混沌动力学对物种共存的中介作用近年来得到了广泛的关注，但寄生物和种群结构对物种平衡共存的中介作用可能更为突出。在宿主-寄生虫系统竞争、共存和进化的背景下，研究者研究了内生真菌的共存和进化，寄生虫介导的共存和竞争，以及猎物-捕食者-寄生虫的相互作用。利用结构种群模型，他研究了：结构宿主种群中寄生虫毒力的进化，结构捕食-猎物系统中的表观Allee效应，以及两栖动物多态性的进化。新出现和再出现的传染病以及生物恐怖主义的危险使人们对宿主-寄生虫系统重新产生了兴趣。传染病不仅影响人类及其食物来源（家畜和农用植物），而且也影响天然动植物种群，这一事实使人们注意到寄生虫在生态系统和维持生物多样性方面的重要而迷人的作用。研究宿主-寄生虫的数学模型增强了我们对进化的总体认识，特别是对宿主和寄生虫的进化（毒力的进化，宿主和寄生虫的共同进化）。这些模型有助于设计疾病控制策略，避免寄生虫耐药性和降低寄生虫毒力（毒力管理）。它们还带来了与物种保护相容的环境管理策略。它们可以被用作研究生和本科生教学的教育工具，并与科学界、公共卫生官员和受过教育的公众进行有效的沟通。

Thieme The investigator undertakes mathematical studies ofquestions arising in ecology and population biology, focusing onhost-parasite systems and structured populations. With theirrapid turnover, parasitic populations are ideal objects to studythe principles of evolution; in turn, it is important tounderstand these principles to control infectious diseaseseffectively. Mathematical models and their analysis are verymuch needed for a deeper understanding and as a theoreticallaboratory to devise control and management strategies. In fact,many of the arguments on the adaptive dynamics of virulence havebecome so complex that they can be more easily formulatedmathematically than verbally. While the health aspects ofparasite-host interactions are of immediate concern, their impacton biological diversity may be as important. The mediation ofspecies coexistence through chaotic dynamics has gained a lot ofattention recently, but coexistence at equilibrium mediated byparasites and by population structure may be far more prominent.In the context of competition, coexistence, and evolution inhost-parasite systems, the investigator studies: Coexistence and evolution of endophytic fungi, Parasite mediated coexistence and competition, and Prey-predator-parasite interactions.Using structured population models, he studies: The evolution of parasite virulence in structured host populations, Apparent Allee effects in structured predator-prey systems, and The evolution of polymorphism in amphibians. Emerging and re-emerging infectious diseases and the dangerof bioterrorism have led to a renewed interest in host-parasitesystems. The fact that infectious diseases afflict not onlyhumans and their food sources (domestic animals and agronomicplants), but also natural animal and plant populations, hasdirected attention to the important and fascinating role ofparasites in ecosystems and in the maintenance of biologicaldiversity. Studying mathematical host-parasite models enhancesour insight in evolution in general and in evolution of hosts andparasites in particular (evolution of virulence, co-evolution ofhosts and parasites). These models help to design diseasecontrol strategies that avoid parasite resistance and decreaseparasite virulence (virulence management). They also lead toenvironmental management strategies that are compatible withspecies preservation. They can be used as educational tools ingraduate and undergraduate instruction and for effectivecommunication with the scientific community, public healthofficers, and an educated public audience.