We propose a minimal model defining the relationship between glucose and insulin with the added influence of food intakes. The constructed model consists of a system of 3 nonlinear ordinary differential equations (ODEs). The solutions of our model for both normal and diabetic subjects are compared with a minimal model and a maximal model representing the same relationship. We found that the outputs of our model are similar to those from the minimal and maximal models for both normal and diabetic subjects; the are 0.9997 and 0.9922, respectively, when compared with the minimal model, and are 0.9995 and 0.9940, respectively, when compared with the maximal model. Moreover, the relative errors between solutions are at most 0.9035% and as low as on average when compared with the minimal model for normal subjects and at most 1.331% and as low as 0.1159% on average for diabetic subjects. The discrepancy between our model and the maximal model are at most 1.590% and 5.453% for normal and diabetic subjects, respectively, with a relative error averaging 0.2138% and 0.9002% for normal and diabetic subjects, respectively.

中文翻译：

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食物动力学影响的葡萄糖-胰岛素关系通用最小模型

我们提出了一个最小模型，该模型定义了葡萄糖和胰岛素之间的关系以及食物摄入的额外影响。构建的模型由 3 个非线性常微分方程 (ODE) 组成。我们的模型对正常和糖尿病受试者的解决方案与代表相同关系的最小模型和最大模型进行了比较。我们发现我们模型的输出与正常和糖尿病受试者的最小和最大模型的输出相似。与最小模型相比，分别为 0.9997 和 0.9922，与最大模型相比，分别为 0.9995 和 0.9940。此外，解之间的相对误差最大为 0.9035%，低至与正常受试者的最小模型相比，平均为 1.331%，糖尿病受试者平均低至 0.1159%。对于正常和糖尿病受试者，我们的模型和最大模型之间的差异分别最多为 1.590% 和 5.453%，正常和糖尿病受试者的相对误差分别为 0.2138% 和 0.9002%。