On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics

TLDR

Ordinary differential equations are widely used to model dynamic processes, especially in infectious disease research, and determining unknown parameters requires identifiability analysis, which remains under development for nonlinear models. This article reviews identifiability analysis methodologies for nonlinear ODE models developed over the past one to two decades. The review covers structural, practical, and sensitivity‑based identifiability techniques, and briefly discusses advanced topics and ongoing research. Illustrative examples from HIV, influenza, and hepatitis viral dynamics demonstrate how these methods are applied in practice.

Abstract

Ordinary differential equations (ODE) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last 2 decades, ODEs have also emerged as a prevailing tool in various biomedical research fields, especially in infectious disease modeling. In practice, it is important and necessary to determine unknown parameters in ODE models based on experimental data. Identifiability analysis is the first step in determing unknown parameters in ODE models and such analysis techniques for nonlinear ODE models are still under development. In this article, we review identifiability analysis methodologies for nonlinear ODE models developed in the past one to two decades, including structural identifiability analysis, practical identifiability analysis and sensitivity-based identifiability analysis. Some advanced topics and ongoing research are also briefly reviewed. Finally, some examples from modeling viral dynamics of HIV, influenza and hepatitis viruses are given to illustrate how to apply these identifiability analysis methods in practice.