糖尿病学中使用的数学模型和数据的批判性综述。

A critical review of mathematical models and data used in diabetology.

作者信息

Boutayeb A, Chetouani A

机构信息

Department of Mathematics Faculty of Sciences, Oujda, Morocco.

出版信息

Biomed Eng Online. 2006 Jun 29;5:43. doi: 10.1186/1475-925X-5-43.

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.

摘要

关于糖尿病数学建模的文献极为丰富。在过去几十年间,各种各样的模型被用于糖尿病的不同方面,包括葡萄糖和胰岛素动力学、管理与并发症预防、策略的成本及成本效益以及总体糖尿病流行病学。关于用于糖尿病特定方面的数学模型,定期会发表几篇综述。在本文中,我们对涉及糖尿病诸多方面并使用各种工具的数学模型进行全面概述。该综述同时涵盖了简单和/或全面、确定性和/或随机性、连续和/或离散的模型;这些模型使用常微分方程、偏微分方程、最优控制理论、积分方程、矩阵分析和计算机算法。

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