Nonlinear Dynamics in Structured Biological and Epidemiological Models

点击翻译按钮获取中文摘要

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.