Chaos synchronization and Nelder-Mead search for parameter estimation in nonlinear pharmacological systems: Estimating tumor antigenicity in a model of immunotherapy

Nikhil Pillai, Morgan Craig, Aristeidis Dokoumetzidis, Sorell L. Schwartz, Robert Bies, Immanuel Freedman

Research output: Contribution to journalArticle

2 Scopus citations


In mathematical pharmacology, models are constructed to confer a robust method for optimizing treatment. The predictive capability of pharmacological models depends heavily on the ability to track the system and to accurately determine parameters with reference to the sensitivity in projected outcomes. To closely track chaotic systems, one may choose to apply chaos synchronization. An advantageous byproduct of this methodology is the ability to quantify model parameters. In this paper, we illustrate the use of chaos synchronization combined with Nelder-Mead search to estimate parameters of the well-known Kirschner-Panetta model of IL-2 immunotherapy from noisy data. Chaos synchronization with Nelder-Mead search is shown to provide more accurate and reliable estimates than Nelder-Mead search based on an extended least squares (ELS) objective function. Our results underline the strength of this approach to parameter estimation and provide a broader framework of parameter identification for nonlinear models in pharmacology.

Original languageEnglish (US)
Pages (from-to)23-30
Number of pages8
JournalProgress in Biophysics and Molecular Biology
StatePublished - Nov 2018



  • Chaos synchronization
  • Immunotherapy
  • Nonlinear models
  • Parameter estimation
  • Parameter identifiability

ASJC Scopus subject areas

  • Biophysics
  • Molecular Biology

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