The literature dealing with mathematical modelling for diabetes is abundant. During the last decades, a variety of models have been devoted to different aspects of diabetes, including glucose and insulin dynamics, management and complications prevention, cost and cost-effectiveness of strategies and epidemiology of diabetes in general. Several reviews are published regularly on mathematical models used for specific aspects of diabetes. In the present chapter we propose a selected review of mathematical models dealing with many aspects of diabetes and using various tools. The review includes, side by side, models which are simple and/or comprehensive; deterministic and/or stochastic; continuous and/or discrete; using ordinary differential equations, partial differential equations, optimal control theory, integral equations, matrix analysis and computer algorithms. This review concentrates specifically on mathematical models dealing with glucose homeostasis, using HbA1c and interaction between beta-cell mass, alpha cell mass, insulin, glucagon, glucose, insulin receptors, Free Fatty Acids (FFA), growth hormone and leptin.

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Mathematical Modelling for Glucose Homeostasis and Associated Mechanisms: A State-of-the-Art Review

  • Mohamed E. N. Lamlili,
  • Wiam Boutayeb,
  • Abdesslam Boutayeb

摘要

The literature dealing with mathematical modelling for diabetes is abundant. During the last decades, a variety of models have been devoted to different aspects of diabetes, including glucose and insulin dynamics, management and complications prevention, cost and cost-effectiveness of strategies and epidemiology of diabetes in general. Several reviews are published regularly on mathematical models used for specific aspects of diabetes. In the present chapter we propose a selected review of mathematical models dealing with many aspects of diabetes and using various tools. The review includes, side by side, models which are simple and/or comprehensive; deterministic and/or stochastic; continuous and/or discrete; using ordinary differential equations, partial differential equations, optimal control theory, integral equations, matrix analysis and computer algorithms. This review concentrates specifically on mathematical models dealing with glucose homeostasis, using HbA1c and interaction between beta-cell mass, alpha cell mass, insulin, glucagon, glucose, insulin receptors, Free Fatty Acids (FFA), growth hormone and leptin.