Novel Statistical Methods for Modeling Population Dynamical Systems

数学模型已越来越多地纳入传染病研究，以便对病毒感染和疾病过程提供定量的了解。在数学模型中，常微分方程（ODE）是一个简单而强大的框架，用于建模复杂系统的动力学。ODE模型中的参数通常具有科学意义。在这一领域的大多数研究都集中在从单个对象估计ODE参数上。这不是一种有效的方法，因为数据通常是在多个主题上收集的。该项目的目标是通过结合来自多个主题的数据来开发分析ODE系统的有效方法。预计该研究将在生物医学、生态学和其他科学领域产生广泛影响和应用。在考虑到受试者之间的差异的同时，将考虑能够表征人口共同特征的模型。模型选择的有效方法也将被研究。将开发统计理论和计算算法来解决这一领域的挑战。本研究结果将为现有方法提供新的见解，并为利用ODE模型分析复杂动态系统提供新的研究思路。将进行广泛的数值研究，这将有助于感兴趣的研究人员更好地理解所提出的方法。该研究将与各种教育活动相结合，这些活动将影响与动态建模相关的教与学。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Mathematical models have been increasingly integrated in infectious disease studies in order to provide a quantitative understanding of virus infection and disease processes. Among the mathematical models, the ordinary differential equation (ODE) is a simple but powerful framework for modeling the dynamics of complex systems. Parameters in ODE models often have scientific meanings. Most of the previous research in this area focused on estimating ODE parameters from a single subject. This is not an efficient approach, because the data are often collected on multiple subjects. The objective of this project is to develop efficient methods for analyzing ODE systems by combining data from multiple subjects. The proposed research is expected to have broad impacts and application in biomedical studies, ecology, and other scientific areas.Models that can characterize the common features in the population will be considered while taking into account the variations among subjects. Efficient approaches for model selection will also be investigated. Both statistical theory and computational algorithm will be developed to tackle challenges in this area. Results from this research will provide new insight into the existing methods and inspire new lines of investigations in analyzing complex dynamic systems using ODE model. Extensive numerical studies will be conducted, which will help interested researchers better understand the proposed methods. The research will be integrated with various educational activities that will impact teaching and learning related to dynamic modeling.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.