# Practical identifiability of mathematical models of biomedical processes

## DOI:

https://doi.org/10.26577/jmmcs-2017-3-479## Keywords:

practical identifiability, dynamic systems, сonfidence interval method, inverse problem## Abstract

The paper is devoted to a numerical study of the uniqueness and stability of problems of

determining the parameters of dynamical systems arising in pharmacokinetics, immunology,

epidemiology, sociology, etc. by incomplete measurements of certain states of the system at fixed

time. Significance of parameters difficult to measure is very high in many areas, as their definition

will allow physicians and doctors to make an effective treatment plan and to select the optimal set

of medicines. Due to the fact that the problems under consideration are ill-posed, it is necessary to

investigate the degree of ill-posedness before its numerical solution. One of the most effective ways

is to study the practical identifiability of systems of nonlinear ordinary differential equations that

will allow us to establish a set of identifiable parameters for further numerical solution of inverse

problems. The paper presents three methods for investigating practical identifiability: the Monte

Carlo method, the matrix correlation method, and the confidence intervals method. It is presented

two mathematical models of the pharmacokinetics of the C-peptide and unidentifiable parameters

were determined using the PottersWheel and AMIGO software packages. The similarity of results

is shown, and also the advantages of each of the packages are demonstrated. This investigation

will allow us to construct a regularized unique solution of the inverse problem.

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## How to Cite

*Journal of Mathematics, Mechanics and Computer Science*,

*95*(3), 105–118. https://doi.org/10.26577/jmmcs-2017-3-479