Published September 7, 2016 | Version v1
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A DISCRETE MODEL OF GLUCOSE-INSULIN INTERACTION AND STABILITY ANALYSIS

Authors/Creators

  • 1. Sacred Heart College, Tirupattur, Vellore, Tamilnadu

Description

The stability of a discrete-time Glucose Insulin interaction system is considered in this paper. The system is modeled with difference equations. Local stability conditions about the equilibrium points are obtained. The phase portraits are obtained for different sets of parameter values. Also bifurcation diagrams are provided for selected range of parameter. Numerical simulations are carried out and graphs are also generated to indicate the role of insulin in the regulation process of glucose in the human body.

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References

  • 1. Ackerman E, Gatewood L C, Rosevaer J W & Molnar G D, “Model studies of blood-gluocse regulation”, Bull Math Biophys, 27, Suppl: 21–Suppl:37, 1995.
  • 2. Bolie V W, “Coefficients of normal blood glucose regulation”, J Appl. Physiol, 16, 783 – 788, 1961.
  • 3. Chen C, Tsai H & Wong S, “Modelling the physiological glucose-insulin dynamic system on diabetes”, J Theor. Biol, 265, 314 – 322, 2010.
  • 4. Derouich M & Boutayeb A, “The effect of physical exercise on the dynamics of glucose and insulin”, J Biomech, 35, 911 – 917, 2002.
  • 5. Dubey B & Hussain J, “Models for the effect of environmental pollution on forestry resources with time delay”, Nonlinear Analysis: Real world Applications, 5, 549 – 570, 2004.
  • 6. Giang D V, Lenbury Y, De Gaetano A & Palumbo P, “Delay model of glucose-insulin systems: global stability and oscillated solutions conditional on delays”, J Math Anal Appl, 343, 996 – 1006, 2008.
  • 7. Jamal Hussain and Denghmingliani Zadeng, “A mathematical model of glucose-insulin interaction”, Sci Vis, Vol 14, Issue No 2, April-June 2014.
  • 8. Saber N. Elaydi, “An Introduction to Difference Equations”, Third Edition, Springer International Edition, First Indian Reprint, 2008.
  • 9. Xiaoli Liu, Dongmei Xiao, “Complex dynamic behaviors of a discrete-time predator - prey system”, Chaos, Solitons and Fractals 32, 80 – 94, 2007.