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越来越多的挑战。各种非本土媒介(如蚊子)的移动导致了流行病和登革热、疟疾和西尼罗河病毒等人类疾病的传播。西尼罗河病毒不仅是对人类健康的威胁，也是对当地生态系统的威胁，因为这种引入的病原体可能会导致脆弱的本土物种灭绝，造成可能在整个生态系统中蔓延的有害影响。生态系统也可能直接受到某些动物入侵者的破坏。一个例子是梭子鱼，这是大沼泽地的一种非本土鱼类，可以迁徙到淡水沼泽，捕食小型饲料鱼，否则会支持涉水鸟类群落。抗菌素耐药细菌的出现是另一种类型的生物入侵，由抗菌素耐药细菌引起的感染是对公共健康的严重威胁。因此，有必要拥有模拟工具来预测这种入侵的空间扩散和影响。这些生物学和流行病学问题中的每一个都可以通过使用结构化的人口模型来研究，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。这个项目的目标是构建这样的预测工具，并调查基本的结构变量(例如，年龄、大小、成熟程度、位置、潜伏期)如何影响这些入侵系统的属性和相关的流行病学结果。该项目的目标是：(I)研究西尼罗河病毒在美国的传播动力学，探索有用和有效的预防措施。根据西尼罗河病毒传播的特点和特点，将采用常微分方程模型和结构化模型。(2)开发空间结构模型，以调查环境污染对医院耐药细菌临床流行病学的作用，重点是卫生保健人员、患者和环境之间的相互作用。(3)通过建立和分析对流-反应-扩散模型，研究小型食鱼性鱼类对佛罗里达湿地南部淡水湿地景观的入侵。由于各种结构模型可以写成抽象的半线性方程，因此我们将研究具有非稠密区域的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.