文章基本信息

标题：Optimal selection of injection doses and injection timings for insulin therapy in a limited time
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作者：Shouzong Liu ; Ling Yu ; Mingzhan Huang 等
期刊名称：Advances in Difference Equations
印刷版ISSN：1687-1839
电子版ISSN：1687-1847
出版年度：2020
卷号：2020
期号：1
页码：1-23
DOI：10.1186/s13662-020-03111-z
出版社：Hindawi Publishing Corporation
摘要：In this paper, we study the injection strategies of insulin for the impulsive therapy of diabetes in a limited time. According to whether we consider the risk of hypoglycemia or not, we develop two different control objectives and investigate three different injection strategies for each control objective. We apply a time-rescaling method to overcome technical obstacles in optimal impulsive control and compute the gradient formulas of cost functions with respect to injection doses and injection timings. By means of numerical simulations we get the optimal injection doses and injection timings for each injection strategy. Our study indicates that for the control objective without considering the risk of hypoglycemia, the optimal injection timing control is more effective than the optimal injection dose control, whereas the mixed control achieves almost the same effect as the optimal injection timing control. For the other control objective considering the risk of hypoglycemia, the optimal injection timing control performs better than the optimal injection dose control in avoiding emergence of hypoglycemia, and the mixed control provides the best strategy in preventing hyperglycemia from occurrence.
关键词：Insulin therapy ; Optimal control ; Injection dose ; Injection timing