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Sib. Zh. Ind. Mat., 2020, Volume 23, Number 1, Pages 107–125 (Mi sjim1081)  

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

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


DOI: https://doi.org/10.33048/SIBJIM.2020.23.110

Full text: PDF file (917 kB)
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UDC: 519.6
Received: 27.06.2019
Revised: 19.09.2019
Accepted:05.12.2019

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

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}


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  • Сибирский журнал индустриальной математики
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