Local stability analysis of glucose-insulin dynamics with Michaelis-Menten kinetics - Catulpos, Ruselle G. (College of Science, University of the Philippines Cebu, 2022)
Diabetes is one of the leading cause of deaths worldwide and it is also a major cause of many other diseases such as heart attacks, blindness, and kidney failure among others. Diabetes is a disease where there is an abnormal production or usage of insulin that regulates the glucose level in one?s body. In this study, we propose a two-dimensional nonlinear ordinary differential equation to model glucose and insulin interaction with the presence of Michaelis-Menten functional response as the insulin-dependent glucose uptake. The proposed model is developed by modifying Zadeng?s work [28] incorporating the Michaelis-Menten functional response in Li and Kuang?s study [19]. Linearization approach and trace-determinant plane analysis was utilized to classify the equilibrium point of the system and to study the stability of the equilibrium point. The results of the study show that the system has a unique and locally asymptotically stable equilibrium point. Additionally, we vary the parameter values α3, α4 and b1 that represents the constant increase of glucose concentration released by the liver, the Michaelis-Menten constant, and the constant rate of insulin production due to glucose stimulation, respectively, to determine its significant effects to the dynamics of glucose and insulin in the model.