A Mathematical Model for Glucose-Insulin Interaction under the Influence of Externally Ingested Glucose in Presence of Constant Amount of Glucose and Insulin in the Body

Authors

  • Ranjan Kalita  Department of Mathematics, Assam down town University, Guwahati, Assam, India
  • Anuradha Devi  Department of Mathematics, Assam Royal Global University, Guwahati, Assam, India

Keywords:

Modelling, Mathematical Modelling, Diabetes Mellitus, Glucose-Insulin Regulatory System, Stability, Lyapunov Function

Abstract

Here, we prepare a mathematical model for glucose- insulin regulation having been influenced by externally ingested glucose. It is also assumed that constant amount of glucose and insulin are always present in the body. This model is a modification of the G-I-E model [14] considering the constant amount of insulin in the body. The stability of the model is analysed by construction of Lyapunov function and conditions for stability have been derived. The model is also analysed numerically to observe the behaviour of the glucose-insulin regulation.

References

  1. E. Ackerman, L.C. Gatewood, J. W. Rosevaer, G. D. Molnar, "Model studies of blood-glucose regulation", Bull Math Biophys, (1965), 27, suppl: 21-suppl: 37.
  2. E. Ackerman, J. W. Rosevaer, G. D. Molnar, "Concepts and models of Biomathematics", F. Itemets, Marcel Dekker, (1969), 131-156.
  3. M. A. Ali, P. S. Uduman, "Mathematical model related to human life expectancy", International journal of Mathematics and Statistics Invention (JIMSI), (2014), 2(3), 08-13.
  4. American diabetes association, "Diabetes PhD and Archimedes", (2003).
  5. V. W. Bolie, "Coefficients of normal blood glucose regulation", J Appl. Physical, (1961), 16: 783-788
  6. R. N. Bergman, Y. Z. Ider, C. R. Bowden, C. Cobelli, "Quantitative estimation of insulin sensitivity", Am. J Biophysics, (1979), 236, E667-E677.
  7. R. N. Bergman, C. R. Bowden, C. Cobelli, "The Minimal Model approach to quantification of factors controlling glucose disposal in man", Carbohydrate Metabolism, vol. 13. Edited by Cobelli, Bergman. John Wiley & Sons Ltd., (1981), 13,269-293
  8. R. N. Bergman, "Minimal model: Perspective from 2005", Hormone Research, (2005), 64(3), 8-15.
  9. C. Cobelli, K. Thomaseth, "Optimal input design for identification of compartmental models: theory and applications to a model of glucose kinetics" Mathematical Biosciences, (1985) 77,267-270.
  10. C. Cobelli, K. Thomaseth, "The minimal model of glucose disappearance: optimal input studies", Math Biosciences, (1987), 83,127-130.
  11. C. Cobelli, K. Thomaseth, "An optimality of the impulse input for linear system identification", Math Biosciences, (1988), 89,127-129.
  12. C. Cobelli, K. Thomaseth, "Optimal equidose inputs and role of measurement error for estimating the parameters of a compartmental model of glucose kinetics from continuous and discrete time optimal examples", Math Biosciences, (1989), 89,135-137.
  13. C. Cobelli, A. Mari, "Validation of mathematical models complex endocrine- metabolism systems: a case study on a model of glucose regulation", Med. and Biot. Eng. and Comput. (1983), 21, 390-399.
  14.  A. Devi, R. Kalita, A. Ghosh, "A mathematical model of Glucose-Insulin regulation under the influence of externally ingested glucose.(G-I-E) model", IJMSI, (2016): ,4, 54-58.
  15. "Global Report on Diabetes", WHO, (2016)
  16. H. P. Himsworth, R. B. Ker, "Insulin–sensitive and insulin insensitive types of diabetes mellitus", CliSci, (1939), 4: 119-122.
  17. A. Makroglou, J. Li, Y. Kuang , "Mathematical software tools for the glucose insulin regulatory system and diabetes: an overview", Applied Numerical Mathematics, (2006), 56, 559-573
  18. A. Makroglou, I. Karaoustas, "A review on delay differential equation models in diabetes modeling, II. The insulin therapies and the intracellular activities of beta cells case", (May 18, 2011)
  19. A. Boutayeb, A. Chetouani, "A critical review of mathematical models and data used in diabetology", Bio medical engineering online, (2006), 5, 43.
  20. G. Pacini, R. N. Bergman, "MINMOD: A computer program to calculate insulin sensitivity and pancreatic responsively from frequently sampled intravenous glucose tolerance test. Computer Methods and Programs in Biomedicine", (1986), 23, 113-122.
  21. R. Srinivasan, A. H. Kadish, R. Sridhar, "A mathematical model for the control mechanism of free-fatty acid and glucose metabolism in normal humans", (1970), Comp. Biomed. Res, 3,146-149.

International Journal of Scientific Research in Science, Engineering and Technology

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Published

2018-08-30

Issue

Volume 4, Issue 9, July-August-2018

Section

Research Articles

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How to Cite

[1]
Ranjan Kalita, Anuradha Devi, " A Mathematical Model for Glucose-Insulin Interaction under the Influence of Externally Ingested Glucose in Presence of Constant Amount of Glucose and Insulin in the Body, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 4, Issue 9, pp.507-511, July-August-2018.