Mathematical modeling and qualitative analysis of insulin therapies

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50 Scopus citations


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
Issue number1
StatePublished - Nov 2007


  • 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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