Spatial nonuniformity of the environment is important in the survival or extinction of many large-scale ecological and epidemiological systems. This project studies how movement of organisms in the environment affects ecosystem survival or epidemic outbreak/extinction. Examples of such movement include dispersal of marine larvae between different reefs under water flow, spreading of infectious diseases via holiday travel or environmental pathogen movement, and infection through movement of insects that carry disease. Several user-friendly quantitative indices and their computation will be introduced to biologists and other scientists as tools for detecting and preventing ecological extinction or epidemic outbreaks. The research will model and optimize the effect of vaccination, medical treatment, and quarantine in epidemic events, and harvesting and harvesting restrictions for agricultural/fishery/forestry systems, to provide answers to important questions about sustaining high quality living environments and preventing epidemic outbreaks. Sample applications of the proposed research include (a) preventing cholera epidemics spreading through a common water source and (b) restoring Chesapeake Bay oyster populations. The outcomes from application projects will provide actionable strategies for government agencies, and the results will improve economic productivity of fisheries.
The impact of spatial heterogeneity and dispersal on key ecological indices and properties will be quantitatively defined and calculated, and a unified mathematical framework will be developed to study the persistence, stability and control of both single and interacting species in heterogeneous environment or networks. The focus is the impact of asymmetric movement on the dynamical behavior of the biological systems, and infusing graph theory, matrix theory and their continuous counterparts into the study of corresponding dynamical systems is a key to the new theory. Several classical concepts in dynamical systems and mathematical biology such as Lyapunov stability theory, basic reproduction number, maximum sustainable yield and a new concept of target reproduction number will be defined in a broader context and analyzed with the additional network structure and spatial heterogeneity. The project will train graduate students and undergraduate students, and the modeling skills and new mathematical techniques that students acquire from the project will make them part of a future workforce with strong quantitative and analytical ability.
