TY - JOUR

T1 - Practical identifiability of mathematical models of biomedical processes

AU - Kabanikhin, Sergey

AU - Bektemesov, Maktagali

AU - Krivorotko, Olga

AU - Bektemessov, Zholaman

N1 - Funding Information: This work was supported by the grant 075-15-2019-1078 (MK-814.2019.1) of the President of the Russian Federation and by the grant AP09260317 of the Ministry of Education and Science of the Republic of Kazakhstan. Publisher Copyright: © 2021 Institute of Physics Publishing. All rights reserved.

PY - 2021/12/20

Y1 - 2021/12/20

N2 - 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 methods for investigating practical identifiability: the Monte Carlo method, the matrix correlation method, the confidence intervals method and the sensitivity based method. There is presented two mathematical models of the pharmacokinetics of the C-peptide and mathematical model of the spread of the COV ID − 19 epidemic. The identifiability investigation will allow us to construct a regularized unique solution of the inverse problem.

AB - 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 methods for investigating practical identifiability: the Monte Carlo method, the matrix correlation method, the confidence intervals method and the sensitivity based method. There is presented two mathematical models of the pharmacokinetics of the C-peptide and mathematical model of the spread of the COV ID − 19 epidemic. The identifiability investigation will allow us to construct a regularized unique solution of the inverse problem.

UR - http://www.scopus.com/inward/record.url?scp=85123993586&partnerID=8YFLogxK

U2 - 10.1088/1742-6596/2092/1/012014

DO - 10.1088/1742-6596/2092/1/012014

M3 - Conference article

AN - SCOPUS:85123993586

VL - 2092

JO - Journal of Physics: Conference Series

JF - Journal of Physics: Conference Series

SN - 1742-6588

IS - 1

M1 - 012014

T2 - 11th International Scientific Conference and Young Scientist School on Theory and Computational Methods for Inverse and Ill-posed Problems

Y2 - 26 August 2019 through 4 September 2019

ER -