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Cited by 610Control Systems and IdentificationMathematical and Theoretical Epidemiology and Ecology ModelsStatistical and numerical algorithms

On Identifiability of Nonlinear ODE Models and Applications in Viral Dynamics

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Miao, Hongyu, Xia, Xiaohua, Perelson, Alan S., Wu, Hulin·2011·SIAM Review
DOI 10.1137/090757009PMC PMC3140286
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Abstract

Ordinary differential equations (ODEs) are a powerful tool for modeling dynamic processes with wide applications in a variety of scientific fields. Over the last two 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 determining 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 couple of 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 and influenza viruses are given to illustrate how to apply these identifiability analysis methods in practice.

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  • StructuralIdentifiability.jl enables identifiability analysis for Catalyst models.

    “This is enabled through the StructuralIdentifiability.jl package.”

    From Catalyst: Fast and flexible modeling of reaction networks (2023) · cites this paper as [58]

    Section 3 discusses methods for structural identifiability analysis, but does not address the StructuralIdentifiability.jl package or its use with Catalyst models. Searches for the package name, Catalyst, and Julia returned no passage establishing the claimed software capability. (LLM, conf=0.76)

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Cited by

Sorted by citations

Authors
Miao, H., Xia, X., Perelson, A. S., & Wu, H.
Affiliations
  • University of Rochester Medicine (US)
  • University of Pretoria (ZA)
  • Los Alamos National Laboratory (US)
ORCID
Venue
SIAM Review
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Published
2011-01
Volume
53
Issue
1
Pages
3-39
ISSN
  • 0036-1445 (ISSN-L)
  • 1095-7200
DOI
10.1137/090757009
PMC
PMC3140286
OpenAlex
W2113105229
Cited by
610
References
5
Citations by year
2026: 39 · 2025: 49 · 2024: 59 · 2023: 49 · 2022: 60 · 2021: 54 · 2020: 49 · 2019: 39 · 2018: 45 · 2017: 30 · 2016: 36 · 2015: 20 · 2014: 26 · 2013: 27 · 2012: 14
FWCI
40.27
Type
journal article
Language
en
Open access
Locations
  • SIAM Review (publishedVersion)
  • PubMed (publishedVersion)
  • PubMed Central (acceptedVersion)
  • UpSpace Institutional Repository (University of Pretoria) (submittedVersion)
Funders
  • National Institutes of Health (n01ai50020-7-0-0)
  • National Institute of Allergy and Infectious Diseases (N01-AI-050020, R37AI028433, R01AI028433, R01AI055290, P30AI078498)
  • National Center for Research Resources (R01RR006555)
Topics
  • Physical Sciences › Engineering › Control and Systems Engineering › Control Systems and Identification
  • Health Sciences › Medicine › Public Health, Environmental and Occupational Health › Mathematical and Theoretical Epidemiology and Ecology Models
  • Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
Keywords
identifiability analysis, nonlinear ordinary differential equations, structural identifiability, practical identifiability, parameter estimation, viral dynamics, HIV, influenza, hepatitis viruses, epidemic modeling

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