Glucose-insulin concentration in the body has continued to elicit research in the field of mathematics. Higher glucose in the body causes diabetes, a chronic disease, if not well managed can lead to death. The present study presents a mathematical model formulating the concentration of glucose and insulin. The well-posedness of the system indicated that the proposed model is applicable in real-life applications. The study is guided by the basic reproductive number, which shows if the concentration of glucose in the body is stable or unstable. A sensitivity analysis showed the constant rate of insulin-dependent glucose disappearance is the most sensitive in the model. The study results observed that the quantity of the assumed insulin infused into the body to regulate glucose concentration is insufficient to manage glucose concentration. Thus, optimal control of the system suggests an increase in the constant rate of insulin-dependent glucose disappearance could be effective after 5 hours of study. Future studies need to consider including other parameters, such as glucose accelerated loss due to exercise in the system.