# Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview

@article{Makroglou2006MathematicalMA, title={Mathematical models and software tools for the glucose-insulin regulatory system and diabetes: an overview}, author={A. Makroglou and Jiaxu Li and Y. Kuang}, journal={Applied Numerical Mathematics}, year={2006}, volume={56}, pages={559-573} }

An overview of some of the mathematical models appearing in the literature for use in the glucose-insulin regulatory system in relation to diabetes is given, enhanced with a survey on available software. The models are in the form of ordinary differential, partial differential, delay differential and integro-differential equations. Some computational results are also presented.

#### 357 Citations

Numerical Applications for Insulin Treatment Models

- Computer Science
- 2011

Two models for dynamics of the insulin and glucose concentration for diabetic human patients are investigated and a minimal one with two compartments and the second one is obtained by introducing a reaction term are investigated. Expand

Bivariate Stochastic Modelling of Glucose and Insulin Regulatory System among Type -2 Diabetes Mellitus Patients

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In this paper, a bivariate stochastic model for glucose and insulin regulatory system is developed. Difference Differential equations are derived from the processes of arrival and consumption of… Expand

A review on delay differential equation models in diabetes modeling , II : the insulin therapies and the intracellular activities of β-cells case

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This is a sequel to the paper by Makroglou et al (2010) which gave a review of diabetes modeling in the form of delay differential equations associated with ultradian oscillations and the intravenous… Expand

A model for the hepatic glucose metabolism based on Hill and step functions

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- J. Comput. Appl. Math.
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We propose a system of first-order ordinary differential equations to describe and understand the physiological mechanisms of the interplay between plasma glucose and insulin and their behaviors in… Expand

Nonlinear Physiological Model of Insulin-Glucose Regulation System in Type 1 Diabetes Mellitus

- Medicine
- 2019

The results here are in accordance with previous ones and indicating that insulin-glucose regulating system has many dynamics in different situations, which may be helpful for better understanding of diabetes mellitus regulation system. Expand

Glucose insulin system software for therapeutic management of diabetes in humans

- Engineering
- 2013

In this research work, a computer program was developed using the gut-blood system model as an infinite number of continuous stirred tanks in series and visual basic application tools, where… Expand

A New Time-Delay Model for Chaotic Glucose-Insulin Regulatory System

- Computer Science
- Int. J. Bifurc. Chaos
- 2020

A new time-delay mathematical model is proposed for glucose-insulin endocrine meta-metabolism and its application in noninvasive investigation of glucose- Insulin interaction is proposed. Expand

Mathematical modeling and qualitative analysis of insulin therapies.

- Biology, Medicine
- Mathematical biosciences
- 2007

The analytical results show the existence and uniqueness of a stable periodic solution that corresponds to ultradian insulin secretion oscillations in a delay differential equation model used for insulin therapies. Expand

ODE models for the management of diabetes: A review

- Medicine
- International Journal of Diabetes in Developing Countries
- 2016

Diabetes also known as diabetes mellitus is a chronic and complex metabolic disease due to the persistent raised blood glucose concentration for long duration. The mechanism behind the disturbed… Expand

Mathematical Models of Insulin-Glucose Regulation: an Important Tool for a Better Understanding of Diabetes

- 2013

A number of mathematical models relating to diabetes have grown in complexity during the last decade as new aspects of the disease are discovered and added into each model. Traditional models for… Expand

#### References

SHOWING 1-10 OF 85 REFERENCES

Mixed graphical models for simultaneous model identification and control applied to the glucose-insulin metabolism.

- Mathematics, Medicine
- Computer methods and programs in biomedicine
- 1998

In this paper a method for model identification of biological systems described by stochastic linear differential equations using a new computational technique for statistical Bayesian inference,… Expand

An adaptive plasma glucose controller based on a nonlinear insulin/glucose model

- Mathematics, Medicine
- IEEE Transactions on Biomedical Engineering
- 1994

An appropriate nonlinear model of the insulin/glucose regulatory system into an adaptive controller should predict the insulin-dependent glucose removal more reliably and hence provide better control over a wide spectrum of insulin signals. Expand

Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin

- Mathematics, Computer Science
- Appl. Math. Comput.
- 2004

This paper proposes a model which incorporates this time delay explicitly and proves theorems on positivity, boundedness, persistence and global asymptotic stability. Expand

Mathematical modelling of the intravenous glucose tolerance test

- Mathematics, Medicine
- Journal of mathematical biology
- 2000

It is concluded that a global unified model of the glucose-insulin system is both theoretically desirable and practically usable, and that any such model ought to undergo formal analysis to establish its appropriateness and to exclude conflicts with accepted physiological notions. Expand

The intravenous route to blood glucose control.

- Medicine, Computer Science
- IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society
- 2001

Close-loop blood glucose regulation algorithms that use the intravenous route for insulin delivery to insulin-dependent diabetic patients and classical control methods and advanced algorithms using implicit knowledge or explicit models are examined are examined. Expand

The subcutaneous route to insulin-dependent diabetes therapy.

- Medicine
- IEEE engineering in medicine and biology magazine : the quarterly magazine of the Engineering in Medicine & Biology Society
- 2001

The authors review the subcutaneous closed- and partially closed-loop strategies that have been proposed and tested in recent years for insulin-dependent diabetes therapy. Expand

A fully symbolic design and modeling of nonlinear glucose control with Control System Professional Suite (CSPS) of Mathematica.

- Computer Science, Medicine
- Acta physiologica Hungarica
- 2004

A fully symbolic design and modeling method is presented for blood glucose control of diabetic patients under intensive care using Mathematica based on a modified two-compartment model proposed by Bergman et al. Expand

Mathematical modeling in glucose metabolism and insulin secretion

- Biology, Medicine
- Current opinion in clinical nutrition and metabolic care
- 2002

Mathematical models in the study of glucose metabolism, insulin secretion and the insulin-glucose interactions are reviewed, with particular emphasis on the methods for the assessment of insulin sensitivity and insulin secretion. Expand

Coefficients of normal blood glucose regulation.

- Chemistry, Medicine
- Journal of applied physiology
- 1961

A previously formulated glucose-insulin feed-back theory was simplified with appropriate assumptions for the purpose of determining which physiological sensitivity coefficients dominate the mathema...

A Model of β -Cell Mass, Insulin, and Glucose Kinetics: Pathways to Diabetes

- Chemistry
- 2000

Abstract Diabetes is a disease of the glucose regulatory system that is associated with increased morbidity and early mortality. The primary variables of this system are β -cell mass, plasma insulin… Expand