Novel Statistical Methods for Modeling Population Dynamical Systems

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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.