Dynamical Systems in Parasite-Host and Structured Population Models

Thieme 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，重点是宿主-寄生虫系统和结构化种群。 寄生虫种群更新迅速，是研究进化原理的理想对象，而了解这些原理对于有效控制传染病具有重要意义。 数学模型及其分析是非常需要的，以加深理解，并作为一个理论实验室，以制定控制和管理策略。 事实上，许多关于毒力适应动力学的争论已经变得如此复杂，以至于它们可以更容易地用数学公式表达而不是口头表达。 虽然寄生虫-宿主相互作用的健康方面是直接关注的问题，但它们对生物多样性的影响可能同样重要。 通过混沌动力学调解物种共存最近得到了很多关注，但由寄生虫和种群结构介导的平衡共存可能更加突出。在宿主-寄生虫系统中的竞争，共存和进化的背景下，研究者研究：内生真菌的共存与进化，寄生虫介导的共存与竞争，和猎物-捕食者-寄生虫相互作用。使用结构化种群模型，他研究：结构化宿主种群中寄生虫毒力的演变，结构化捕食者-猎物系统中的表观Allee效应，以及两栖动物中多态性的演变。 新出现和重新出现的传染病和生物恐怖主义的蔓延导致了对宿主-寄生虫系统的新的兴趣。 传染病不仅危害人类及其食物来源（家畜和农业植物），而且危害自然界的动物和植物种群，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。 研究数学宿主-寄生虫模型增强了我们对一般进化，特别是宿主和寄生虫进化（毒力进化，宿主和寄生虫共同进化）的洞察力。 这些模型有助于设计避免寄生虫抗性和降低寄生虫毒力（毒力管理）的疾病控制策略。 它们还导致环境管理战略与物种保护兼容。 它们可以作为教育工具用于研究生和本科生教学，并与科学界，公共卫生官员和受过教育的公众有效沟通。

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.