Parameters identification in the mathematical model of immune competition cells
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Abstract
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.
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'
© 2015 by De Gruyter
Articles in the same Issue
- Frontmatter
- The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity
- Ill-conditioning versus ill-posedness for the boundary controllability of the heat equation
- Parameters identification in the mathematical model of immune competition cells
- Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations
- Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses
- An inverse problem for the Vlasov–Poisson system
- An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method
- Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms
- The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation
Articles in the same Issue
- Frontmatter
- The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity
- Ill-conditioning versus ill-posedness for the boundary controllability of the heat equation
- Parameters identification in the mathematical model of immune competition cells
- Inverse source problems for time-fractional mixed parabolic-hyperbolic-type equations
- Model parameter estimation of linear time-invariant systems from combined data of forced and initial condition responses
- An inverse problem for the Vlasov–Poisson system
- An inexact Newton regularization in Banach spaces based on the nonstationary iterated Tikhonov method
- Multilevel preconditioning for sparse optimization of functionals with nonconvex fidelity terms
- The first solution of a long standing problem: Reconstruction formula for a 3-d phaseless inverse scattering problem for the Schrödinger equation
