Nonlinear Dynamics in Structured Biological and Epidemiological Models

人类健康和生态系统的完整性面临着来自生物入侵的日益严峻的挑战。各种非本地病媒（如蚊子）的移动导致登革热、疟疾和西尼罗河病毒等人类疾病的流行和传播。西尼罗病毒不仅对人类健康构成威胁，而且对本地生态系统也构成威胁，因为这种引入的病原体可能导致脆弱的本地物种灭绝，从而在整个生态系统中产生连锁反应的有害影响。生态系统也可能被某些动物入侵者直接破坏。一个例子是梭鱼，这是大沼泽地的一种非本地鱼类，它可以迁徙到淡水沼泽，捕食小饲料鱼，否则这些鱼会支持涉水鸟类群落。耐药细菌的出现是另一种类型的生物入侵，由耐药细菌引起的感染是严重的公共卫生威胁。因此，必须有模拟工具来预测这种入侵的空间扩散和影响。这些生物和流行病学问题中的每一个都可以通过使用结构化人口模型来研究，以确定个人的出生、生长和死亡率以及他们与环境和彼此之间的相互作用。该项目的目标是构建这样的预测工具，并调查基本结构变量（例如，年龄、大小、成熟度水平、位置、潜伏期）如何影响这些侵入性系统的特性和相关的流行病学结果。该项目的目标是：(1)研究西尼罗河病毒在美国的传播动态，探索有用和有效的预防措施。根据西尼罗病毒传播的特点和特点，将采用常微分方程模型和结构模型。㈡建立空间结构模型，调查环境污染对医院耐抗生素细菌临床流行病学的作用，重点关注保健工作者、患者和环境之间的相互作用。(3)通过构建和分析平流-反应-扩散模型，调查佛罗里达南部沼泽淡水景观中小型食鱼鱼类的入侵情况。由于各种结构模型可以写成抽象的半线性方程，因此将研究非密集域半线性方程的非线性动力学，并将理论结果应用于具体的生物学和流行病学问题。

Human health and the integrity of ecosystems face increasing challenges from biological invasions. The movement of various nonindigenous vectors (e.g., mosquitoes) has resulted in epidemics and the spread of human diseases such as dengue, malaria, and West Nile virus. West Nile virus is a not only a threat to human health, but also to native ecosystems, since vulnerable native species can be driven into extinction by this introduced pathogen, creating detrimental effects that can cascade through an ecosystem. Ecosystems may also be disrupted directly by certain animal invaders. An example is the pike killifish, a non-native fish in the Everglades that can migrate into freshwater marshes and prey on the small forage fishes that would otherwise support the wading bird community. The emergence of antimicrobial-resistant bacteria is another type of biological invasion and infections caused by antimicrobial-resistant bacteria are a serious public health threat. Thus, it is essential to have simulation tools to forecast the spatial spread and effects of such invasions. Each of these biological and epidemiological problems can be studied by using structured population models to determine the birth, growth and death rates of individuals and their interactions with the environment and with each other. The goal of this project is to construct such forecasting tools and to investigate how the essential structuring variables (e.g., age, size, maturity level, location, latency) affect the properties of these invasive systems the associated epidemiological outcomes.The goals of this project are: (i) Study the transmission dynamics of West Nile virus in the U.S. and explore useful and effective prevention measures. Based on the features and characteristics on the transmission of West Nile virus, both ordinary differential equation models and structured models will be applied. (ii) Develop spatially-structured models to investigate the role of environmental contamination on the clinical epidemiology of antibiotic-resistant bacteria in hospitals focusing on the interactions between health-care workers, patients and the environment. (iii) Investigate the invasion by small piscivorous fish in freshwater marsh landscapes in the southern Florida Everglades by constructing and analyzing advection-reaction-diffusion models. Since various structured models can be written as abstract semilinear equations, the nonlinear dynamics of semilinear equations with non-dense domain will be studied and the theoretical results will be applied to specific biological and epidemiological problems.