Wang Haiyan, Li Jiaxu, Kuang Yang
Department of Mathematical Sciences and Applied Computing, Arizona State University, Phoenix, AZ 85069-7100, USA.
Math Biosci. 2007 Nov;210(1):17-33. doi: 10.1016/j.mbs.2007.05.008. Epub 2007 May 29.
Several insulin therapies are widely in clinical use with the basic strategy that mimics insulin secretion in a normal glucose-insulin endocrine metabolic regulatory system. In this paper, we model the insulin therapies using a delay differential equation model. We study the dynamics of the model both qualitatively and quantitatively. The analytical results show the existence and uniqueness of a stable periodic solution that corresponds to ultradian insulin secretion oscillations. Numerically we simulate the insulin administration based on our model. The numerical simulation results are in agreement with findings of clinical studies.
几种胰岛素疗法在临床上广泛使用，其基本策略是模拟正常葡萄糖 - 胰岛素内分泌代谢调节系统中的胰岛素分泌。在本文中，我们使用延迟微分方程模型对胰岛素疗法进行建模。我们对该模型的动力学进行了定性和定量研究。分析结果表明存在一个稳定的周期解，它对应于超日胰岛素分泌振荡，并且该解是唯一的。我们基于我们的模型对胰岛素给药进行了数值模拟。数值模拟结果与临床研究结果一致。
