# Modelling Glucose-Insulin Dynamics: Insights for Diabetes Management

## Keywords:

Stability, Initial Conditions, Glucose-Insulin, Regulatory System, Diabetic Patient, Dynamical System## Abstract

**Communication in Physical Sciences, 2024, 11(3): 382-397**

**Author:** Amadi Ugwulo Chinyere

*Received: 26 January 2024/Accepted: 10 May 2024*

This study presents a comprehensive review and critical analysis of mathematical models used in glucose-insulin regulatory systems, with a focus on their application in diabetes research and clinical practice. The review highlights the strengths and limitations of existing models, emphasizing the need for further refinement and validation to enhance their predictive accuracy and clinical utility. Additionally, recommendations for future research directions are provided, emphasizing the importance of interdisciplinary collaborations and the translation of mathematical models into practical tools for personalized diabetes management. Overall, this work contributes to the advancement of mathematical modelling in diabetes research and underscores its potential to improve patient care and outcomes.

### Downloads

## References

Ahren, B. & Pacini, G. (2004). Importance of quantifying insulin secretion in relation to insulin sensitivity to accurately assess beta cell function in clinical studies. Eur J. Endrocinol., 150, 2, pp 97-104.

Amadi,U.C.& Ekaka-a, E.N.(2017).Modeling the vulnerability of poor data reporting in the design of glucose-insulin diabetics. IJPAS.Cambridge Research and Publications Vol.9 No.1.

Baker, C. T. H. & Rahan, F. A. (1999). Sensitivity analysis of parameter in modeling with delay differential equations, MCCM Numerical Analysis Report, 349, Manchester University.

Bennett, D. L. & Gourly, S. A. (2004). Asymptotic properties of a delay differential equation model for the interaction of glucose with plasma and interstitial insulin, Appl. Math. Comp. 151, pp. 189-207.

Bergman, R. N. (2002). Pathogenesis and prediction of diabetes mellitus: Lessons from integrative physiology in: Irving L. Schwartz lecture, Mount Sinai J Medicine 60, pp. 280- 290.

Bergman, R. N. & Cobelli, C. (1980). Minimal modeling, partition analysis and the estimation of insulin sensitivity, Federation Proc. 39, pp. 110-115.

Bergman, R. N., Philips, L. S. & Cobelli C. (1981). Physiologic evaluation of factors controlling glucose tolerance in man: measurement of insulin sensitivity and beta-cell glucose sensitivity from the response to intravenous glucose. J. Clin Invest, 68, 6, pp. 1456 - 1467.

Bertram, R., Satin, L., Zhang, M., Smolen, P., and Sherman, A. (2004) Calcium and glycolysis ediate multiple bursting modes in pancreatic islets, Biophys. J. 87, 3074-3087.

Breen, L., Philip A., Shaw C. S., Jeukendrup A. E., Baar K. and Tipton K. D. (2011). Beneficial effects of resistance exercise on glycemic control are not further improved by protein ingestion, Plos one, 6( 6) e20613.

Bolie, V.W. (1961). Coefficients of normal blood glucose regulation, J. Appl. Physiol, 16, pp. 783- 788.

Cobelli, C., Dalla Man, C., Sparacino, G., Magni, L., De Nicolao, G. & Kovatchev, B. P. (2009). Diabetes: Models, signals and control, IEEE. Reviews in biomedical Engineering, 2, https://www.researchgate.net/publication/47385208.

De Gaetano, A. & Arino, O. (2000). Mathematical modeling of the intravenous glucose test Journal of Math. Biol., 40, 136-168.

Derouich, M. & Boutayeb, A. (2002). The effect of physical exercise on the dynamics of glucose and insulin, J. Biomech. 35(7): 911-917.

Devi, A., Kalita, R. and Ghosh, A. (2016). An interactive glucose- insulin regulation under the influence of externally ingested glucose (GIG-I-E) model. Global Journal of Mathematical Sciences: Theory and Practical. ISSN0974-3200 9(3): 277-285.

Engelborghs, K., Lemaire, V., Belair, J. and Roose, D. (2001). Numerical bifurcation analysis of differential equations arising from physiological modeling, J. Math, Bio. 42, 361-385.

Ekaka-a, E. N., Nwachukwu, E.C., Nafo, N. M. and Amadi, E. H. (2013). Stabilization methods for two dis-similar biogas solids population system with higher carrying capacities, IOSR Journal of mathenatics, e-ISSN: 2278- 5728, 2319- 765X, 7(6) 58-60.

Godsland, I. F., (2003). The minimal model: An evolving methodology. Comment on behalf of the editorial board. Clinical sch. 105, pp. 531-532.

Gyorgy, A., Kovacs, L., Haidegger, T. & Benyo, B. (2009). Investigating a novel model of human blood glucose system at molecular levels from control theory. http://wwwresearchgate.net/publication.

Keener, J. P. & Sneyder, J. (1998). Mathematical physiology, Springer, Berlin, 1998.

Kuperstein, R. and Sasson, Z. (2000). Effects of antihypertensive therapy on glucose and insulin metabolism and on left ventricular mass: a randomnized, double-blind, controlled study of 21 obese hypertensives. Circulation, 102, 15, pp. 1802-1806.

Leticia, O. and Oleka, L. N. (2016). Mathematical model for the dynamic behavior of two competing plant species, International Journal of Scientific and Research Publications, 6, 5, pp. 498- 502.

Li, J., Kuang, and Li, B. (2006). Analysis of IVGTT glucose-insulin interaction models with time delay. Discrete Contin. Dyn. Sys. Ser. B1, pp. 103-124.

Makroglou, A., Li, J. and Kuang, Y. (2006). Mathematical models and software tools for the glucose- insulin regulatory system and diabetes: an overview, Applied Numerical Mathematics, 56, pp. 559-573.

May, R. M. and Leonard (1975). Nonlinear aspects of competition between three species, SIAM Journal of Applied Mathematics, 29, pp. 243-253.

Randomski, D., Lawrynczuk, M., Marusak, P. M. and Biocybernetics, P. T. (2010) Biomedical Engineering, 30, pp. 41-53-872.

Rao, G. S., Bajaj, J. S. and Rao, J. S. (1997) Mathematical modeling of insulin kinetics, Current Science, 73, 11, pp. 957-967.

Sandhya and Kumar, D. (2011). Mathematical model for glucose-insulin regulatory system of diabetes mellitus. Advances in Applied Mathematical Biosciences, 2, 1,, pp. 39-46

Sturis, J., Polonsky, K. S., Mosekilde, E. & VanCauter, E. (1991). Computer-model for mechanism underlying ultradian oscillations of insulin and glucose, Amer. J. Physiol. Endocrinol. Metab., 260, pp. E801-E809.

Toffolo, G., bergman, R. N., Finegood, D. T., Bowden, C. R. & Cobelli, C. (1980). Quantitative estimation of beta cell sensitivivity to glucose in the intact organism: A minimal mode of insulin kinetics in the dog, Diabetes, 29, 12, pp. 979-990.

Tolic, I. M., Mosekilde, E. & Sturis, J. (1999). Modeling the insulin-glucose feedback system: The significance of pulsatile insulin secretion. J. Theor. Biol. 207, pp. 361-375.

Yan, Y., Coca, O. & Barbu (2008). Feedback control for Navier-Stokes equation, Nonlinear Functional Analysis and Optimization, 29, pp. 225- 242.

Yan, Y., Coca, O. & Barbu V. (2009). Finite-dimensional controller design for semi linearparabolic systems, Nonlinear Analysis: Theory Methods and Applications, 70, pp. 4451- 4475.

## Downloads

## Published

## Issue

## Section

## License

Copyright (c) 2024 Journal and Author

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.