Mathematical Modeling of Intra-Venous Glucose Tolerance Test Model With Two Discrete Delays

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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“…Pitchaimani et.al [38] considered a two discrete delay for IVGTT model, they showed that in theory, the IVGTT model [6] is best fitting for all existing data. But our model shows that, it satisfies not only the existing data also the 40 subjects (for the minimum range R 1 and the maximum range R 2 , the parameters estimate from the WLS model) [35] ISSN: 2456-8686, Volume 1, Issue 1, 2017:1-30 DOI : http://doi.org/10.26524/cm1…”

“…In [36], we consider for each α > 0, the bnanach space of fading memory type, Proposition 2.1 As in [38], the time derivatives of the postibe solutions (5) are bounded.…”

“…The following Table III contains the eigen value for the unique positive steady states. The values γ is taken from [33] and other parameter values are taken from [38]. Here R1 and R2 denote the minimum and maximum range values for 40 subjects healthy volunteers and these values are taken from [35].…”

Analysis of Pathogen-Immune Interaction Dynamics with Three Time delays

“…The initial conditions for system (2) are chosen at t = 0 as Theorem 2.1 All solutions of system (2) are positive and bounded in C + , for all t > 0. Furthermore, all solutions eventually enter and remain in the following bounded region:…”

“…Many works have been developed for various infectious diseases using different types of delay differential equation models [1,2,3,4,5,6,7,13,14]. Simple models are useful for verifying the various hypotheses and for determining the method of medical treatments.…”