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
Digital Object Identifier (DOI)
A. Rihan, Fathalla; A. Azamov, Abdulla; and J. Al-Sakaji, Hebatallah
"An Inverse Problem for Delay Differential Equations: Parameter Estimation, Nonlinearity, Sensitivity,"
Applied Mathematics & Information Sciences: Vol. 12
, Article 6.
Available at: https://dc.naturalspublishing.com/amis/vol12/iss1/6