Measure-valued analysis of stochastic populations

该项目旨在开发新的数学模型和工具，用于严格分析受内部竞争和反馈影响的非常普遍的随机种群。所提出的数学框架是测量值过程的框架，这是一种需要包含此类系统固有的复杂性和随机结构的设置。这类模型在进化生物学、细胞动力学和癌症研究中有实际应用，对我们理解地方病的持久性和濒危物种的保护至关重要。该项目的结果有望提供对复杂随机种群的行为和稳定性的洞察，并为其管理提供指导。

The project aims to develop new mathematical models and tools for the rigorous analysis of very general stochastic populations that are subject to internal competition and feedback. The proposed mathematical framework is that of measure-valued processes, a setting needed to encompass the complexity and random structure inherent in such systems. Models of this kind have real-world applications in evolutionary biology, cell kinetics and cancer research, and are essential to our understanding of the persistence of endemic disease and of the preservation of endangered species. The results of this project are expected to provide insight into the behaviour and (in-)stabilities of complex stochastic populations, and offer guidance for their management.