Nonlinear Dynamics in Structured Biological and Epidemiological Models

University Of Miami, Coral Gables FL

Investigators

Abstract

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.