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Study of Two Time Delays in IVGTT Glucose–Insulin Dynamical System

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Abstract

Time delays occurred in insulin secretion and its action play a vital role in maintaining the glucose level in diabetics. Li et al. proposed a model by considering a time delay occurred in insulin secretion from pancreas stimulated by raised glucose concentration. After insulin secretion, a delay is occur in insulin action to lower the raised glucose concentration. To meet with the physiology of human body, the model given by Li et al. has been extended by incorporating a second time delay occurred in insulin action. Stability analysis has been done for the extended model and it possesses positive solutions. From the simulation results, we conclude that sustained periodic oscillations are observed for both of the time delays. Also, the simulations shows that after introducing the delay in insulin action, the delay length of insulin secretion proposed by Li et al. has been shortened, which can be proved important in maintaining the glucose level after delivery of insulin.

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Acknowledgements

We acknowledge Delhi Technological University, Delhi for the financial support.

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  1. Department of Applied Mathematics, Delhi Technological University, Delhi, 110042, India

    Saloni Rathee &  Nilam

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  1. Saloni Rathee
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  2. Nilam
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Correspondence to Nilam.

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Rathee, S., Nilam Study of Two Time Delays in IVGTT Glucose–Insulin Dynamical System. Int. J. Appl. Comput. Math 3 (Suppl 1), 1337–1346 (2017). https://doi.org/10.1007/s40819-017-0421-6

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  • DOI: https://doi.org/10.1007/s40819-017-0421-6

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