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Observability and Structural Identifiability of Nonlinear Biological Systems

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  • Alejandro F. Villaverde

Abstract

Observability is a modelling property that describes the possibility of inferring the internal state of a system from observations of its output. A related property, structural identifiability, refers to the theoretical possibility of determining the parameter values from the output. In fact, structural identifiability becomes a particular case of observability if the parameters are considered as constant state variables. It is possible to simultaneously analyse the observability and structural identifiability of a model using the conceptual tools of differential geometry. Many complex biological processes can be described by systems of nonlinear ordinary differential equations and can therefore be analysed with this approach. The purpose of this review article is threefold: (I) to serve as a tutorial on observability and structural identifiability of nonlinear systems, using the differential geometry approach for their analysis; (II) to review recent advances in the field; and (III) to identify open problems and suggest new avenues for research in this area.

Suggested Citation

  • Alejandro F. Villaverde, 2019. "Observability and Structural Identifiability of Nonlinear Biological Systems," Complexity, Hindawi, vol. 2019, pages 1-12, January.
    • Handle: RePEc:hin:complx:8497093
    DOI: 10.1155/2019/8497093
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    References listed on IDEAS

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    1. Alejandro F Villaverde & Antonio Barreiro & Antonis Papachristodoulou, 2016. "Structural Identifiability of Dynamic Systems Biology Models," PLOS Computational Biology, Public Library of Science, vol. 12(10), pages 1-22, October.
    2. Ryan N Gutenkunst & Joshua J Waterfall & Fergal P Casey & Kevin S Brown & Christopher R Myers & James P Sethna, 2007. "Universally Sloppy Parameter Sensitivities in Systems Biology Models," PLOS Computational Biology, Public Library of Science, vol. 3(10), pages 1-8, October.
    3. Walter, Eric & Lecourtier, Yves, 1982. "Global approaches to identifiability testing for linear and nonlinear state space models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 24(6), pages 472-482.
    4. Maria Pia Saccomani & Karl Thomaseth, 2018. "The Union between Structural and Practical Identifiability Makes Strength in Reducing Oncological Model Complexity: A Case Study," Complexity, Hindawi, vol. 2018, pages 1-10, February.
    5. Denis-Vidal, Lilianne & Joly-Blanchard, Ghislaine & Noiret, Céline, 2001. "Some effective approaches to check the identifiability of uncontrolled nonlinear systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 57(1), pages 35-44.
    6. Nicolette Meshkat & Christine Er-zhen Kuo & Joseph DiStefano III, 2014. "On Finding and Using Identifiable Parameter Combinations in Nonlinear Dynamic Systems Biology Models and COMBOS: A Novel Web Implementation," PLOS ONE, Public Library of Science, vol. 9(10), pages 1-14, October.
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    1. Nerea Martínez & Alejandro F. Villaverde, 2020. "Nonlinear Observability Algorithms with Known and Unknown Inputs: Analysis and Implementation," Mathematics, MDPI, vol. 8(11), pages 1-27, October.
    2. Inmaculada López & Zoltán Varga & Manuel Gámez & József Garay, 2022. "Monitoring in a Discrete-Time Nonlinear Age-Structured Population Model with Changing Environment," Mathematics, MDPI, vol. 10(15), pages 1-16, July.

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