Mathematical modeling and qualitative analysis of insulin therapies

Research output: Contribution to journalArticle

37 Citations (Scopus)

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 2007

Fingerprint

Insulin
qualitative analysis
Qualitative Analysis
Mathematical Modeling
Therapy
mathematical models
insulin secretion
insulin
secretion
modeling
Secretion
dynamic models
oscillation
clinical trials
Therapeutics
glucose
Delay Differential Equations
Glucose
Model
insulin replacement therapy

Keywords

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

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Ecology, Evolution, Behavior and Systematics

Cite this

Mathematical modeling and qualitative analysis of insulin therapies. / Wang, Haiyan; Li, Jiaxu; Kuang, Yang.

In: Mathematical Biosciences, Vol. 210, No. 1, 11.2007, p. 17-33.

Research output: Contribution to journalArticle

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