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Journal of Inverse and Ill-posed Problems

Editor-in-Chief: Kabanikhin, Sergey I.

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Volume 23, Issue 4


Parameters identification in the mathematical model of immune competition cells

Lekbir Afraites / Abdelghafour Atlas
Published Online: 2015-01-15 | DOI: https://doi.org/10.1515/jiip-2014-0012


This paper deals with the problem of identifying parameters in the mathematical model of immune competition developed in [Modelling Complex Biological Systems: A Kinetic Theory Approach, Birkhäuser, Boston, 2006]. More precisely, we use the approach called inverse problem to identify the parameters of the model, and we investigate the identifiability as well as the stability of the inverse problem. In numerical analysis, the inverse problem is reformulated as an optimization problem where the variables are the estimated parameters in the model. In our study, the regularized least-squares cost function and the adjoint technique to compute the gradient of the cost function are used. Finally, some numerical tests for parameters identification using synthetic data are presented.

Keywords: Immune competition cells; inverse problem; parameters identification; identifiability; stability; least squares cost function; Tikhonov regularization; adjoint technique

MSC: 65L09; 65K05; 92B05

About the article

Received: 2014-02-11

Revised: 2014-05-30

Accepted: 2014-11-05

Published Online: 2015-01-15

Published in Print: 2015-08-01

Funding Source: Hassan II Academy of Sciences and Technology (Morocco)

Award identifier / Grant number: Project `Méthodes mathématiques et outils de modélisation et simulation pour le cancer'

Citation Information: Journal of Inverse and Ill-posed Problems, Volume 23, Issue 4, Pages 323–337, ISSN (Online) 1569-3945, ISSN (Print) 0928-0219, DOI: https://doi.org/10.1515/jiip-2014-0012.

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