黄明湛, 刘守宗, 宋新宇, 俞玲, 姚娇艳. 一类带有生理时滞与状态反馈脉冲控制的胰岛素治疗模型研究[J]. 信阳师范学院学报(自然科学版), 2018, 31(4): 520-524. DOI: 10.3969/j.issn.1003-0972.2018.04.002
引用本文: 黄明湛, 刘守宗, 宋新宇, 俞玲, 姚娇艳. 一类带有生理时滞与状态反馈脉冲控制的胰岛素治疗模型研究[J]. 信阳师范学院学报(自然科学版), 2018, 31(4): 520-524. DOI: 10.3969/j.issn.1003-0972.2018.04.002
HUANG Mingzhan, LIU Shouzong, SONG Xinyu, YU Ling, YAO Jiaoyan. Studies on a Insulin Therapy Model with Physiological Delays and State Feedback Impulsive Control[J]. Journal of Xinyang Normal University (Natural Science Edition), 2018, 31(4): 520-524. DOI: 10.3969/j.issn.1003-0972.2018.04.002
Citation: HUANG Mingzhan, LIU Shouzong, SONG Xinyu, YU Ling, YAO Jiaoyan. Studies on a Insulin Therapy Model with Physiological Delays and State Feedback Impulsive Control[J]. Journal of Xinyang Normal University (Natural Science Edition), 2018, 31(4): 520-524. DOI: 10.3969/j.issn.1003-0972.2018.04.002

一类带有生理时滞与状态反馈脉冲控制的胰岛素治疗模型研究

Studies on a Insulin Therapy Model with Physiological Delays and State Feedback Impulsive Control

  • 摘要: 针对糖尿病病人的胰岛素治疗过程,建立了一个带有三个生理时滞以及状态反馈脉冲控制的半连续动力系统.首先对带有时滞的半连续动力系统的解给出其严格的数学定义,然后讨论了所构建系统中血糖浓度的持久性.另外数值分析结果表明,合理设置控制阈值可将血糖水平保持在人体能承受的范围内.胰岛素输送时滞和肝糖原生成时滞越短,血糖控制效果越好,而胰岛素生成时滞的大小对血糖水平几乎无影响.此外,当脉冲注射剂量足够大时,在预设的控制阈值约束下,系统存在周期解,而且胰岛素的注射剂量越大,血糖控制的效果越好,即两次注射的间隔越长且血糖的水平越低.

     

    Abstract: For the insulin therapy of diabetes, an semi-continuous dynamical system with three physiological time delays and state feedback impulsive insulin injection is proposed. A strict mathematical definition of the solution of general delay semi-continuous dynamical system is firstly given. Then the permanence of the glucose concentration in the model is discussed. Besides, numerical analyses show that the reasonable defined control level can maintain the glucose concentration in the range that people can tolerate. Shorter transport delay of insulin and hepatic glucose production delay produce better control effect, while the insulin secretion delay has almost no impact on the glucose level. Furthermore, if the injection dose is large enough, the system has a stable periodic solution under a predefined control threshold, and the control effect is better when the injection dose is larger, that is, the glucose concentration is lower and the period between two injections is longer.

     

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