Nonlinear Dynamics in Structured Biological and Epidemiological Models

在这一建议中，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将研究具有非密集域的半线性方程的非线性动力学，并将其应用于流行病学和种群动力学中的年龄结构模型。其次，PI将考虑非局部平流-反应-扩散方程行波解的存在性。研究结果可应用于描述非局部相互作用和延迟的平流-反应-扩散方程描述的矢量-宿主模型和竞争模型的行波解研究。PI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，项目将调查环境污染对医院耐抗生素细菌临床流行病学的影响，重点是卫生保健工作者、患者和环境之间的相互作用。结构化种群动态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彼此之间和与环境的相互作用。通常，结构变量是年龄（个体的年龄、感染后的时间或细胞分裂后的时间）、大小、成熟度、空间、潜伏期等。结构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和流行病学过程的结果和后果。PI建议研究结构模型的非线性动力学，并将结果应用于传染病的传播动力学研究，如甲型流感、乙型肝炎和一些病媒传播疾病。通过数学建模和分析，项目还将研究环境污染对医院耐药菌临床流行病学的影响，确定细菌感染的因素，寻找有效的控制措施。

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.