Nonlinear Dynamics in Structured Biological and Epidemiological Models

结构化生物和流行病学模型中的非线性动力学

• 批准号: 1022728
• 负责人: Shigui Ruan
• 金额: $ 24万
• 依托单位: University of Miami
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-09-15 至 2014-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1022728&HistoricalAwards=false
• 关键词: Nonlinear; Dynamics; Structured; Biological; Epidemiological

In this proposal, the PI proposes to study the nonlinear dynamics of structured population models and apply the results to investigate some specific biological and epidemiological problems. Firstly, the PI will study the nonlinear dynamics of semilinear equations with non-dense domain and apply to age-structured models in epidemiology and population dynamics. Secondly, the PI will consider the existence of traveling wave solutions of nonlocal advection-reaction-diffusion equations. The main results can be applied to study traveling wave solutions in vector-host models and competition models described by advection-reaction-diffusion equations with spatio-temporal delay, which describes the nonlocal interactions and latency. The PI proposes to investigate the spatio-temporal dynamics of such models and to understand how vector-borne diseases (such as dengue and malaria) and invasive species spread spatially. Thirdly, the PI will investigate the role of environment contamination on the clinical epidemiology of antibiotic-resistant bacteria in hospitals focusing on the interactions between health-care workers, patients and the environment. Structured population dynamics classify individuals according to their characteristics and states (such as age, size, location, status, and movement) to determine the birth, growth and death rates of the populations and their interactions with each other and with environment. Typically, the structuring variables are age (age of the individual, chronological time since infection or time since cell division), size, maturity level, space, latency, etc. The goal of structured population dynamics is to study how these characteristics and states affect the properties of these models and the outcomes and consequences of the biological and epidemiological processes. The PI proposes to investigate nonlinear dynamics of structured models and apply the results to study transmission dynamics of infectious diseases, such as influenza A, hepatitis B, and some vector-borne diseases. Via mathematical modeling and analysis, the PI will also study the role of environment contamination on the clinical epidemiology of antibiotic-resistant bacteria in hospitals, identify factors responsible for bacterial infection, and look for efficient control measures.

在这项建议中，PI建议研究结构种群模型的非线性动力学，并将结果应用于研究一些特定的生物学和流行病学问题。首先，PI将研究具有非稠密区域的半线性方程的非线性动力学，并应用于流行病学和人口动力学中的年龄结构模型。其次，PI将考虑非局部对流-反应-扩散方程的行波解的存在性。主要结果可用于研究具有时空延迟的对流-反应-扩散方程所描述的矢量-宿主模型和竞争模型中的行波解，该方程描述非局部相互作用和延迟。国际和平研究所建议调查这些模型的时空动态，并了解媒介传播的疾病(如登革热和疟疾)和入侵物种如何在空间上传播。第三，PI将调查环境污染对医院耐药细菌临床流行病学的作用，重点是医护人员、患者和环境之间的相互作用。结构化种群动力学根据个体的特征和状态(如年龄、大小、位置、地位和运动)对个体进行分类，以确定种群的出生、生长和死亡率以及它们之间的相互作用和与环境的相互作用。通常，结构变量是年龄(个体的年龄、感染以来的时间或细胞分裂以来的时间)、大小、成熟程度、空间、潜伏期等。结构化种群动力学的目标是研究这些特征和状态如何影响这些模型的特性以及生物学和流行病学过程的结果和后果。PI建议研究结构化模型的非线性动力学，并将其结果应用于研究传染病的传播动力学，如甲型流感、乙肝和一些媒介传播的疾病。通过数学建模和分析，PI还将研究环境污染对医院耐药细菌临床流行病学的影响，找出导致细菌感染的因素，并寻找有效的控制措施。