Sensitivity analysis and practical identifiability of some mathematical models in biology

O. I. Krivorotko ; D. V. Andornaya ; S. I. Kabanikhin

Sibirskij žurnal industrialʹnoj matematiki, Tome 23 (2020) no. 1, pp. 107-125.

Résumé

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.

Détail

Keywords: identifiability, ordinary differential equations, sensitivity matrix, sensitivity analysis, method of correlation matrix, Monte Carlo method, inverse problem.

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