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MATHEMATICAL MODELING OF INTRA-VENOUS GLUCOSE TOLERANCE TEST MODEL WITH TWO DISCRETE DELAYS

M. PITCHAIMANI

Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chennai-5, India

E-mail Address: mpitchaimani@yahoo.com

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P. KRISHNAPRIYA

Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chennai-5, India

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, and

C. MONICA

Ramanujan Institute for Advanced Study in Mathematics University of Madras, Chennai-5, India

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https://doi.org/10.1142/S021833901550031XCited by:1 (Source: Crossref)

Abstract

A mathematical model for Intra-Venous Glucose Tolerance Test (IVGTT) with explicit glucose–insulin interaction is presented as a system of delay differential equation with discrete time delays and its important mathematical features are analyzed. This model includes the positivity and boundedness of the solution. An unique equilibrium point is found and its local stability is investigated. Using the Lyapunov functional approach, we show the global stability of the unique equilibrium point. The length of delay that preserves the stability is estimated. Sensitivity analysis is performed on a delay differential equation model for IVGTT that suggests the parameter value has a major impact on the model dynamics. Numerical calculations are performed to support and elaborate the analytical findings.

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