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Simplified Mathematical Model of Glucose-Insulin System
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
School of Medicine, College of Medicine and Health Sciences, University of Rwanda, Kigali, Rwanda
School of Medicine, College of Medicine and Health Sciences, University of Rwanda, Kigali, Rwanda
School of Medicine, College of Medicine and Health Sciences, University of Rwanda, Kigali, Rwanda
School of Medicine, College of Medicine and Health Sciences, University of Rwanda, Kigali, Rwanda
- 1 Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
- 2 Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
- 3 Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
- 4 Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
- 5 Department of Mathematics, School of Science, College of Science and Technology, University of Rwanda, Kigali, Rwanda
- 6 School of Medicine, College of Medicine and Health Sciences, University of Rwanda, Kigali, Rwanda
- 7 School of Medicine, College of Medicine and Health Sciences, University of Rwanda, Kigali, Rwanda
- 8 School of Medicine, College of Medicine and Health Sciences, University of Rwanda, Kigali, Rwanda
- 9 School of Medicine, College of Medicine and Health Sciences, University of Rwanda, Kigali, Rwanda
American Journal of Computational Mathematics·Volume 08 (2018)·Pages 233–244·Published 31 August 2018·DOI10.4236/ajcm.2018.83019
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Abstract
Mathematical modelling of glucose-insulin system is very important in medicine as a necessary tool to understand the homeostatic control of human body. It can also be used to design clinical trials and in the evaluation of the diabetes prevention. In the last three decades so much work has been done in this direction. One of the most notable models is the global six compartment-mathematical model with 22 ordinary differential equations due to John Thomas Sorensen. This paper proposes a more simplified three compartment-mathematical model with only 6 ordinary differential equations by introducing a tissue compartment comprising kidney, gut, brain and periphery. For model parameter identification, we use inverse problems technique to solve a specific optimal control problem where data are obtained by solving the global model of John Thomas Sorensen. Numerical results show that the proposed model is adaptable to data and can be used to adjust diabetes mellitus type I or type II for diabetic patients.
KeywordsGlucoseInsulinMathematical ModelParameterIdentification
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