@article{Kabanikhin_Bektemessov_Krivorotko_Voronov_2017, title={Practical identifiability of mathematical models of biomedical processes}, volume={95}, url={https://bm.kaznu.kz/index.php/kaznu/article/view/479}, DOI={10.26577/jmmcs-2017-3-479}, abstractNote={<p>The paper is devoted to a numerical study of the uniqueness and stability of problems of<br>determining the parameters of dynamical systems arising in pharmacokinetics, immunology,<br>epidemiology, sociology, etc. by incomplete measurements of certain states of the system at fixed<br>time. Significance of parameters difficult to measure is very high in many areas, as their definition<br>will allow physicians and doctors to make an effective treatment plan and to select the optimal set<br>of medicines. Due to the fact that the problems under consideration are ill-posed, it is necessary to<br>investigate the degree of ill-posedness before its numerical solution. One of the most effective ways<br>is to study the practical identifiability of systems of nonlinear ordinary differential equations that<br>will allow us to establish a set of identifiable parameters for further numerical solution of inverse<br>problems. The paper presents three methods for investigating practical identifiability: the Monte<br>Carlo method, the matrix correlation method, and the confidence intervals method. It is presented<br>two mathematical models of the pharmacokinetics of the C-peptide and unidentifiable parameters<br>were determined using the PottersWheel and AMIGO software packages. The similarity of results<br>is shown, and also the advantages of each of the packages are demonstrated. This investigation<br>will allow us to construct a regularized unique solution of the inverse problem.</p>}, number={3}, journal={Journal of Mathematics, Mechanics and Computer Science}, author={Kabanikhin, S. I. and Bektemessov, Z. M. and Krivorotko, O. I. and Voronov, D. A.}, year={2017}, month={Sep.}, pages={105–118} }