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首页> 外文期刊>Communications in Nonlinear Science and Numerical Simulation >The regulatory system for diabetes mellitus: Modeling rates of glucose infusions and insulin injections
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The regulatory system for diabetes mellitus: Modeling rates of glucose infusions and insulin injections

机译：糖尿病的调节系统：葡萄糖输注和胰岛素注射速率的建模

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Novel mathematical models with open and closed-loop control for type 1 or type 2 diabetes mellitus were developed to improve understanding of the glucose-insulin regulatory system. A hybrid impulsive glucose-insulin model with different frequencies of glucose infusions and insulin injections was analyzed, and the existence and uniqueness of the positive periodic solution for type 1 diabetes, which is globally asymptotically stable, was studied analytically. Moreover, permanence of the system for type 2 diabetes was demonstrated which showed that the glucose concentration level is uniformly bounded above and below. To investigate how to prevent hyperinsulinemia and hyperglycemia being caused by this system, we developed a model involving periodic intakes of glucose with insulin injections applied only when the blood glucose level reached a given critical glucose threshold. In addition, our numerical analysis revealed that the period, the frequency and the dose of glucose infusions and insulin injections are crucial for insulin therapies, and the results provide clinical strategies for insulin-administration practices. (C) 2016 Elsevier B.V. All rights reserved.
机译：开发了具有开环和闭环控制的用于1型或2型糖尿病的新型数学模型，以增进对葡萄糖-胰岛素调节系统的了解。分析了具有不同频率的葡萄糖输注和胰岛素注射的混合脉冲葡萄糖-胰岛素模型，并分析了全球渐近稳定的1型糖尿病正周期解的存在性和唯一性。此外，证实了用于2型糖尿病的系统的持久性，其表明葡萄糖浓度水平上下均匀地界线。为了研究如何预防该系统引起的高胰岛素血症和高血糖症，我们开发了一种模型，该模型涉及定期摄入葡萄糖，仅当血糖水平达到给定的临界葡萄糖阈值时才应用胰岛素注射。此外，我们的数值分析表明，葡萄糖输注和胰岛素注射的时间，频率和剂量对胰岛素治疗至关重要，其结果为胰岛素给药实践提供了临床策略。 （C）2016 Elsevier B.V.保留所有权利。

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