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Sensitivity Analysis and Practical Identifiability of Some Mathematical Models in Biology

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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.

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Funding

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)).

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Authors and Affiliations

  1. Institute of Computational Mathematics and Mathematical Geophysics, pr. Akad. Lavrent’eva 6, Novosibirsk, 630090, Russia

    O. I. Krivorotko

  2. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    D. V. Andornaya

  3. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    S. I. Kabanikhin

Authors
  1. O. I. Krivorotko
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  2. D. V. Andornaya
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  3. S. I. Kabanikhin
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Corresponding authors

Correspondence to O. I. Krivorotko, D. V. Andornaya or S. I. Kabanikhin.

Additional information

Russian Text © The Author(s), 2020, published in Sibirskii Zhurnal Industrial’noi Matematiki, 2020, Vol. 23, No. 1, pp. 107–125.

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Krivorotko, O.I., Andornaya, D.V. & Kabanikhin, S.I. Sensitivity Analysis and Practical Identifiability of Some Mathematical Models in Biology. J. Appl. Ind. Math. 14, 115–130 (2020). https://doi.org/10.1134/S1990478920010123

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  • DOI: https://doi.org/10.1134/S1990478920010123

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