Identifiability and Estimation of Time-Varying Parameters in ODE Models with Applications in Viral Dynamics

• Activity Number: 127
• Type: Contributed
• Date/Time: Monday, August 1, 2011 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Hongyu Miao*+ and Hua Liang and Hulin Wu
• Companies: University of Rochester and University of Rochester and University of Rochester
• Keywords: Ordinary Differential Equation ; Time-varying Parameter ; Identifiability ; Spline-enhanced Nonlinear Least Square ; Viral Dynamics

Abstract

Ordinary differential equations (ODE) are prevailing modeling tools in investigations of viral dynamics such as HIV and influenza virus. Due to the complexity in the inverse problem for nonlinear ODE models, investigators usually consider constant parameters in their models. However, key kinetic parameters in ODE models could have a time-varying nature such that constant coefficients cannot accurately represent the dynamic interactions between model components. In this study, we investigated the identifiability and estimation techniques for time-varying parameters in ODE models. In particular, we combined the implicit function theorem and the differential algebra method to address the identifiability issue and we used the spline-enhanced nonlinear least squares (SNLS) approach to accurately estimate both constant and time-varying parameters in HIV and influenza infection models. We then verified the validity of our approaches via simulation studies. Our methods were also applied to clinical and laboratory data and resulted in interesting biological findings.