Abstract
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 paper we propose a global overview 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.
Highlights
It is commonly admitted that diabetes is sweeping the globe as a silent epidemic largely contributing to the growing burden of non-communicable diseases and mainly encouraged by decreasing levels of activity and increasing prevalence of obesity [1,2,3,4,5]
A variety of mathematical models, statistical methods and computer algorithms have been proposed in order to understand different aspects of diabetes such as: glucose-insulin dynamics, epidemiology of diabetes and its complications, cost of diabetes and cost-effectiveness of strategies dealing with diabetes
These reviews concentrated on specific aspects of diabetes such as glucose-insulin dynamics [713], computer algorithms and devices [14,15,16], sensors and control [17,18], mathematical and software aspects [19], glycemic index [20], burden and cost of diabetes [21,22]
Summary
It is commonly admitted that diabetes is sweeping the globe as a silent epidemic largely contributing to the growing burden of non-communicable diseases and mainly encouraged by decreasing levels of activity and increasing prevalence of obesity [1,2,3,4,5]. Other models of the glucose-insulin dynamics, using optimal control or partial differential equations were proposed by different authors [18,40,41,42,43,44]. As stressed by the Editorial of Diabetes Care [98], functional forms of the equation are given but values of the variables and parts of the model that describe micro- and macro-vascular complications are not provided Beyond these limitations, the model was used to predict 74 major outcomes, giving astounding results: In 71 out of the 74 clinical outcomes, the differences between the results calculated by the model and the observed ones were statistically not significant. In some papers and letters, mathematical models and guidelines for computer modeling of diabetes were subject to debate and criticism [105-107]
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