Bifurcation and Stability Analysis of Glucose-Insulin Regulatory System in the Presence of β-Cells

Diabetes mellitus is one of the most extensive diseases in the world. The mathematical models are prevalent to study the dynamics of glucose, insulin, and beta-cells non-invasively. Therefore, to study the impact of beta-cells on the glucose-insulin regulatory system, a non-linear three-dimensional mathematical model is proposed. The dynamics of the glucose-insulin regulatory system comprising of boundedness of solutions, existence, and stability condition of equilibria are explored theoretically. Additionally, the conditions for saddle-node, transcritical, and Hopf-bifurcation are also examined. The results illustrate that the glucose-insulin regulatory system offers various dynamics in distinct circumstances. The proposed model is in good agreement with the real-life physical significance of glucose-insulin dynamics. Different types of diabetes conditions such as type 2 diabetes and hyperinsulinemia are also observed through the bifurcation analysis.