一类糖尿病模型的动力学行为及敏感性分析

Based on the fact that glucocorticoid induces insulin resistance, a new type of diabetes model involving insulin, glucose, and glucocorticoid was established to explore the complex pathogenesis of diabetes. Firstly, the local and global stability of the equilibrium point was demonstrated with the linearization method, the limit system theory, and the Dulac criterion. Secondly, the key parameters affecting glucose concentration were selected, and the sensitivity analysis of the key parameters with respect to the positive equilibrium point was carried out with the direct differentiation method. This analysis shows how the key parameters influence the secretion and function of insulin and glucocorticoid, thereby helping to regulate the fluctuations of glucose levels. Finally, numerical simulations were conducted on MATLAB. These simulations not only verify the correctness of the theoretical analysis, but also reveal the changing trends of glucose concentrations under different intervention treatments. The results indicate that, the selection of appropriate key parameters is crucial for the control of glucose concentration, which provides a theoretical basis for formulating clinical treatment plans for diabetes.