Novel Statistical Methods for Modeling Population Dynamical Systems

数学模型越来越多地被整合到传染病研究中，以提供对病毒感染和疾病过程的定量了解。在众多的数学模型中，常微分方程是一种简单但功能强大的复杂系统动力学建模框架。常微分方程模型中的参数往往具有科学意义。以往在这一领域的研究大多集中在从单个受试者中估计常数项参数。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。这个项目的目标是开发有效的方法，通过结合来自多个学科的数据来分析ODE系统。这项研究有望在生物医学、生态学和其他科学领域产生广泛的影响和应用。考虑到不同学科之间的差异，将考虑能够表征种群共同特征的模型。还将研究选择模型的有效方法。将开发统计理论和计算算法来应对这一领域的挑战。这一研究结果将为现有方法提供新的见解，并启发使用常微分方程模型分析复杂动态系统的新的研究思路。将进行广泛的数值研究，这将帮助感兴趣的研究人员更好地理解拟议的方法。这项研究将与与动态建模相关的影响教与学的各种教育活动相结合。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.