Stochastic Spatial Models in Ecology

包括生态系统和社会网络在内的生物系统的行为从根本上取决于基本物理环境的空间结构和生物在该环境中的分布，以及生物之间相互作用的性质。这项研究推进了对数学模型的分析，这些模型将提高对重要生物过程的理解，如生物体运动的动力学、传染病的传播和社会网络中信息的扩散。数学技术将与模拟一起使用，以促进对此类系统的了解。这项工作的成果可能会被整合到本科数学和生物课程中。这项研究涉及空间随机模型的研究，这些模型在生物学，特别是生态学中有重要的应用。这个项目将研究人口动力学、传染病传播和社会网络结构模型的相变和限制行为。这些模型将通过包括出生和死亡、竞争和迁移在内的一系列行动纳入粒子之间的相互作用。

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.