报告题目：Modeling impulsive insulin delivery in insulin pump and artificial pancreas

报告时间：2015年6月12日 上午 10:00-11:00

报告地点：数学馆 3楼会议室（310）

报告人：信阳师范学院 宋新宇教授

报告摘要：

In this talk, we propose two novel mathematical models with impulsive injection of insulinor its analogues for type 1 and type 2 diabetes mellitus. One model incorporates the periodic impulsive injection of insulin. We analytically show the existence and uniqueness of a positive globally asymptotically stable periodic solution for type 1 diabetes, which implies that the perturbation caused by insulin injection will not disturb homeostasis but amend the glucose from a pathological level toward a healthier level. We also show that the system is uniformly permanent for type 2 diabetes, that is, the glucose concentration level is uniformly bounded above and below. The other model determines the insulin injection by closely monitoring the glucose level when it reaches or passes a predefined but adjustable threshold value. We analytically prove the existence and stability of the order one periodic solution, which ensures that the perturbation by the injection in such an automated way can keep the blood glucose concentration under control. Our numerical analysis confirms and further enhances the usefulness and robustness of our models. The first model has

clinical implications in that the glucose level of a diabetic can be controlled within a desired level by adjusting the values of two model parameters, injection period and injection dose. A method for choosing these two parameters is described. The second model is, to the best of our knowledge, the first attempt to conquer some critical issues in the design of an artificial pancreas with closed-loop approach. For the former case, our numerical analysis reveals that a regime with a smaller insulin dose and more frequent deliveries is more efficient and effective, but surprisingly, for the latter case, a larger dose is more effective. This can be significant in the design and development of the insulin pump and artificial pancreas

专家简介：

宋新宇，信阳师范学院数学研究所所长，河南省特聘教授。中国林业科学研究院兼职研究员，博士生导师。中国生物数学学会常务理事，《生物数学学报》常务编委；国际期刊《International Journal of Biomathematics》编委；美国数学会《数学评论》评论员；德国数学会《数学文摘》评论员；国家自然科学基金同行评议专家；教育部留学回国人员科研启动基金评审专家。主持国家科学自然基金项目3项，主持河南省高校杰出科研人才创新工程，河南省科技创新杰出人才支持计划等项目。主要从事非线性微分方程及生物动力系统研究，研究领域包括时滞微分方程、脉冲微分方程理论及应用，种群生态与传染病动力学系统等。