In this paper, we have developed a mathematical model of diabetes (type-2 diabetes) in a deterministic approach. We have described our model in the population dynamics with four compartments. Namely, Susceptible, Imbalance Glucose Level (IGL), Treatment and Restrain population. Our model exhibits two nonnegative equilibrium points namely Disease Free Equilibrium (DFE) and Endemic Equilibrium (EE). The expression for the Treatment reproduction number RT is computed. We have proved that the equilibrium points of the model are locally and globally asymptotically stable under some conditions. Numerical simulation is performed to verify our analytical findings such as stability of DFE and EE. The simulations show better results based on the required conditions. We tried to fit our model with the data given by the International Diabetes Federation (IDF) [D. Atlas, IDF Diabetes Atlas, 8th edn. (International Diabetes Federation, Brussels, Belgium, 2017)] and it suits well with the data. It has been found that our model shows the decrease in diabetes-affected population compared with the data given by the IDF [D. Atlas, IDF Diabetes Atlas, 8th edn. (International Diabetes Federation, Brussels, Belgium, 2017)].

中文翻译：

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糖尿病的数学建模及其约束

在本文中，我们以确定性方法开发了糖尿病（2 型糖尿病）的数学模型。我们已经在具有四个隔间的人口动态中描述了我们的模型。即，易感人群、不平衡葡萄糖水平 (IGL)、治疗和限制人群。我们的模型展示了两个非负平衡点，即无病平衡 (DFE) 和地方病平衡 (EE)。治疗再生数的表达式R吨被计算。我们证明了模型的平衡点在某些条件下是局部和全局渐近稳定的。进行数值模拟以验证我们的分析结果，例如 DFE 和 EE 的稳定性。模拟显示基于所需条件的更好结果。我们试图将我们的模型与国际糖尿病联盟 (IDF) [D. 地图集，IDF 糖尿病地图集，第 8 版。（国际糖尿病联盟，布鲁塞尔，比利时，2017 年）]，它与数据非常吻合。已经发现，与 IDF [D. 阿特拉斯，IDF 糖尿病地图集, 第 8 版。（国际糖尿病联盟，布鲁塞尔，比利时，2017 年）]。