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Sibirskii Zhurnal Industrial'noi Matematiki, 2020, Volume 23, Number 1, Pages 107–125
DOI: https://doi.org/10.33048/SIBJIM.2020.23.110 (Mi sjim1081) 		 
This article is cited in 15 scientific papers (total in 15 papers)

Sensitivity analysis and practical identifiability of some mathematical models in biology

O. I. Krivorotkoa, D. V. Andornayab, S. I. Kabanikhinac

a Institute of Computational Mathematics and Mathematical Geophysics SB RAS, pr. Akad. Lavrentieva 6, Novosibirsk 630090, Russia
b Novosibirsk State University, ul. Pirogova 1, Novosibirsk 630090, Russia
c Sobolev Institute of Mathematics SB RAS, pr. Acad. Koptyuga 4, Novosibirsk 630090, Russia
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DOI: https://doi.org/10.33048/SIBJIM.2020.23.110
Abstract: We study the identifiability of some mathematical models of spreading TB and HIV coinfections in a population and the dynamics of HIV-infection at the cellular level. Sensitivity analysis is carried out using the orthogonal method and the eigenvalue method which are based on studying the properties of the sensitivity matrix and show the effect of the model coefficient change on simulation results. Practical identifiability is investigated which determines the possibility of reconstructing coefficients from the noisy experimental data. The analysis is performed using the correlation matrix and Monte Carlo method, while taking into consideration the Gaussian noise in measurements. The results of numerical calculations are presented on whose basis we obtain the identifiable sets of parameters.
Keywords: identifiability, ordinary differential equations, sensitivity matrix, sensitivity analysis, method of correlation matrix, Monte Carlo method, inverse problem.
Funding agency Grant number
Russian Foundation for Basic Research 18-31-20019
Ministry of Education and Science of the Russian Federation МК-814.2019.1
The authors were supported by the Russian Foundation for Basic Research (project no. 18-31-20019) and the Council on Grants of the President of the Russian Federation (Agreement no. 075-15-2019-1078 (MK-814.2019.1)).
Received: 27.06.2019
Revised: 19.09.2019
Accepted: 05.12.2019
English version:
Journal of Applied and Industrial Mathematics, 2020, Volume 14, Issue 1, Pages 115–130
DOI: https://doi.org/10.1134/S1990478920010123
Document Type: Article
UDC: 519.6
Language: Russian
Citation: O. I. Krivorotko, D. V. Andornaya, S. I. Kabanikhin, “Sensitivity analysis and practical identifiability of some mathematical models in biology”, Sib. Zh. Ind. Mat., 23:1 (2020), 107–125; J. Appl. Industr. Math., 14:1 (2020), 115–130
Citation in format AMSBIB
\Bibitem{KriAndKab20}
\by O.~I.~Krivorotko, D.~V.~Andornaya, S.~I.~Kabanikhin
\paper Sensitivity analysis and practical identifiability of some mathematical models in biology
\jour Sib. Zh. Ind. Mat.
\yr 2020
\vol 23
\issue 1
\pages 107--125
\mathnet{http://mi.mathnet.ru/sjim1081}
\crossref{https://doi.org/10.33048/SIBJIM.2020.23.110}
\transl
\jour J. Appl. Industr. Math.
\yr 2020
\vol 14
\issue 1
\pages 115--130
\crossref{https://doi.org/10.1134/S1990478920010123}
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    • This publication is cited in the following 15 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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