Mathematical modeling and qualitative analysis of insulin therapies

Research output: Contribution to journalArticle

39 Scopus citations

Abstract

Several insulin therapies are widely in clinical use with the basic strategy that mimics insulin secretion in a normal glucose-insulin endocrine metabolic regulatory system. In this paper, we model the insulin therapies using a delay differential equation model. We study the dynamics of the model both qualitatively and quantitatively. The analytical results show the existence and uniqueness of a stable periodic solution that corresponds to ultradian insulin secretion oscillations. Numerically we simulate the insulin administration based on our model. The numerical simulation results are in agreement with findings of clinical studies.

Original languageEnglish (US)
Pages (from-to)17-33
Number of pages17
JournalMathematical Biosciences
Volume210
Issue number1
DOIs
StatePublished - Nov 1 2007

Keywords

  • Diabetes
  • Glucose-insulin regulator system
  • Insulin therapy
  • Periodic solution
  • Time delay

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • Biochemistry, Genetics and Molecular Biology(all)
  • Immunology and Microbiology(all)
  • Agricultural and Biological Sciences(all)
  • Applied Mathematics

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