Bifurcation analysis in a delay model of IVGTT glucose-insulin interaction

Fateme Mohabati; MohammadReza Molaei

doi:10.1007/s12064-019-00298-y

Bifurcation analysis in a delay model of IVGTT glucose-insulin interaction

Theory Biosci. 2020 Feb;139(1):9-20. doi: 10.1007/s12064-019-00298-y. Epub 2019 Jul 22.

Authors

Fateme Mohabati¹, MohammadReza Molaei²

Affiliations

¹ Mahani Mathematical Research Center and Department of Pure Mathematics, Shahid Bahonar Kerman University, Kerman, Iran.
² Mahani Mathematical Research Center and Department of Pure Mathematics, Shahid Bahonar Kerman University, Kerman, Iran. mrmolaei@uk.ac.ir.

PMID: 31332694
DOI: 10.1007/s12064-019-00298-y

Abstract

In this paper, a delayed differential model based on the intravenous glucose tolerance test is considered. The conditions to determine stability or instability of the model's steady state are obtained. We obtain the necessary conditions for the appearance of a bifurcation, and we investigate the direction and stability of the local bifurcation. For this purpose, the normal form theory is used. In addition, the numerical diagrams in the direction of theoretical results are drawn.

Keywords: Center manifold; Hopf bifurcation; Stability; Time delay.

MeSH terms

Algorithms
Blood Glucose / analysis*
Computer Simulation
Diabetes Mellitus / blood*
Diabetes Mellitus / diagnosis*
Glucose Tolerance Test / methods*
Humans
Insulin / blood*
Models, Biological
Oscillometry
Reference Values
Time Factors

Substances

Blood Glucose
Insulin