In this research, we present a mathematical model of diabetes mellitus showing how glucose metabolism in the body is related to pancreatic insulin. We looked at the breakdown of glucose due to direct injection of insulin into the vein, and the breakdown of glucose due to the uptake of tissues such as the brain and neurons, and also considered the increased glucose level coming from consuming food and eating glucose directly. From this behavior, we can summarize it as a mathematical model of the system of glucose. Then, we used linear and nonlinear mathematical theorem analysis by Lyapunov’s method with conditional and local stability and global stability cases respectively. Finally, a numerical approach along with a graph presentation was used to confirm the conclusive analysis of the role that insulin works in the process of regulating the blood sugar level in the human body.
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