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Time-Adaptive Determination of Drug Efficacy in Mathematical Model of HIV Infection

Beilina, L. ; Eriksson, M. LU and Gainova, I. (2021) In Differential Equations and Dynamical Systems
Abstract

The paper considers a time-adaptive finite element method for determination of drug efficacy in a parameter identification problem (PIP) for a system of ordinary differential equations (ODE) that describes dynamics of the primary human immunodeficiency virus (HIV) infection with drug therapy. Tikhonov’s regularization method, optimization approach and finite element method to solve this problem are presented. A posteriori error estimates in the Tikhonov’s functional and reconstructed parameter are derived. Based on these estimates a time adaptive algorithm is formulated and numerically tested for different scenarios of noisy observations of virus population function. Numerical results show a significant improvement of reconstruction of... (More)

The paper considers a time-adaptive finite element method for determination of drug efficacy in a parameter identification problem (PIP) for a system of ordinary differential equations (ODE) that describes dynamics of the primary human immunodeficiency virus (HIV) infection with drug therapy. Tikhonov’s regularization method, optimization approach and finite element method to solve this problem are presented. A posteriori error estimates in the Tikhonov’s functional and reconstructed parameter are derived. Based on these estimates a time adaptive algorithm is formulated and numerically tested for different scenarios of noisy observations of virus population function. Numerical results show a significant improvement of reconstruction of drug efficacy parameter using the local time-adaptive mesh refinement method compared to the gradient method applied on a uniform time mesh.

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author
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type
Contribution to journal
publication status
published
subject
in
Differential Equations and Dynamical Systems
publisher
Springer
external identifiers
  • scopus:85107726288
ISSN
0971-3514
DOI
10.1007/s12591-021-00572-w
language
English
LU publication?
no
additional info
Publisher Copyright: © 2021, The Author(s).
id
f42e093f-dc30-4731-93c3-a93f460c89d3
date added to LUP
2023-10-04 10:17:46
date last changed
2023-10-09 16:43:06
@article{f42e093f-dc30-4731-93c3-a93f460c89d3,
  abstract     = {{<p>The paper considers a time-adaptive finite element method for determination of drug efficacy in a parameter identification problem (PIP) for a system of ordinary differential equations (ODE) that describes dynamics of the primary human immunodeficiency virus (HIV) infection with drug therapy. Tikhonov’s regularization method, optimization approach and finite element method to solve this problem are presented. A posteriori error estimates in the Tikhonov’s functional and reconstructed parameter are derived. Based on these estimates a time adaptive algorithm is formulated and numerically tested for different scenarios of noisy observations of virus population function. Numerical results show a significant improvement of reconstruction of drug efficacy parameter using the local time-adaptive mesh refinement method compared to the gradient method applied on a uniform time mesh.</p>}},
  author       = {{Beilina, L. and Eriksson, M. and Gainova, I.}},
  issn         = {{0971-3514}},
  language     = {{eng}},
  month        = {{06}},
  publisher    = {{Springer}},
  series       = {{Differential Equations and Dynamical Systems}},
  title        = {{Time-Adaptive Determination of Drug Efficacy in Mathematical Model of HIV Infection}},
  url          = {{http://dx.doi.org/10.1007/s12591-021-00572-w}},
  doi          = {{10.1007/s12591-021-00572-w}},
  year         = {{2021}},
}