Miao Hongyu, Xia Xiaohua, Perelson Alan S, Wu Hulin
Department of Biostatistics and Computational Biology, University of Rochester School of Medicine and Dentistry, 601 Elmwood Avenue, Box 630, Rochester, New York 14642, USA.
SIAM Rev Soc Ind Appl Math. 2011 Jan 1;53(1):3-39. doi: 10.1137/090757009.
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.
常微分方程（ODE）是用于对动态过程进行建模的强大工具，在各种科学领域有着广泛应用。在过去20年里，常微分方程也已成为各种生物医学研究领域中普遍使用的工具，尤其是在传染病建模方面。在实践中，基于实验数据确定常微分方程模型中的未知参数既重要又必要。可识别性分析是确定常微分方程模型中未知参数的第一步，而针对非线性常微分方程模型的此类分析技术仍在发展之中。在本文中，我们回顾了过去一到二十年中开发的非线性常微分方程模型的可识别性分析方法，包括结构可识别性分析、实际可识别性分析和基于灵敏度的可识别性分析。还简要回顾了一些高级主题和正在进行的研究。最后，给出了一些关于HIV、流感和肝炎病毒病毒动力学建模的例子，以说明如何在实践中应用这些可识别性分析方法。
