Stochastic Spatial Models in Ecology

点击翻译按钮获取中文摘要

The behavior of biological systems including ecosystems and social networks is fundamentally dependent on the spatial structure of the underlying physical environment and distribution of organisms within that environment, as well as the nature of the interactions among the organisms. This research advances the analysis of mathematical models that will improve understanding of important biological processes such as the dynamics of movement of organisms, spread of infectious diseases, and proliferation of information in social networks. Mathematical techniques will be used along with simulations to advance knowledge of such systems. Results arising from this work may be integrated into undergraduate mathematics and biology courses. This research involves the study of spatial stochastic models that have important applications to biology, particularly ecology. This project will investigate phase transitions and limiting behavior of models for population dynamics, infectious disease transmission, and structure of social networks. The models will incorporate the interaction among particles through a number of actions, which include birth and mortality, competition, and migration.