An inverse problem for delay differential equations: Parameter estimation, nonlinearity, sensitivity

Fathalla A. Rihan, Abdulla A. Azamov, Hebatallah J. Al-Sakaji

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

This article presents the theoretical framework to solve inverse problems for Delay Differential Equations (DDEs). Given a parameterized DDE and experimental data, we estimate the parameters appearing in the model, using least squares approach. Some issues associated with the inverse problem, such as nonlinearity and discontinuities which make the problem more ill-posed, are studied. Sensitivity and robustness of the models to small perturbations in the parameters, using variational approach, are also investigated. The sensitivity functions may provide guidance for the modelers to determine the most informative data for a specific parameter, and select the best fit model. The consistency of delay differential equations with bacterial cell growth is shown by fitting the models to real observations.

Original languageEnglish
Pages (from-to)63-74
Number of pages12
JournalApplied Mathematics and Information Sciences
Volume12
Issue number1
DOIs
Publication statusPublished - Jan 1 2018

Keywords

  • Biological systems
  • DDEs
  • Nonlinearity
  • Parameter estimation
  • Sensitivity analysis
  • Time-lags

ASJC Scopus subject areas

  • Analysis
  • Numerical Analysis
  • Computer Science Applications
  • Computational Theory and Mathematics
  • Applied Mathematics

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