Mathematical model for detecting diabetes in blood cells with the influence of cortisol

Diabetes is a disease that occurs when the body is unable to produce enough insulin or cannot use insulin effectively, causing an increase in blood glucose. One of the factors that affect the stability of glucose and insulin is the hormone cortisol, which is produced when the body experiences stress. The purpose of this study is to develop a mathematical model of diabetes detection in blood cells by considering the influence of cortisol. The model is formulated as a system of linear differential equations and analyzed through equilibrium points and eigenvalue analysis. The results show that two eigenvalues form asymptotically stable spirals, while the other two are asymptotically stable nodes, indicating system stability. The novelty of this study lies in the inclusion of cortisol, which delays stabilization of glucose–insulin dynamics and provides a more realistic representation of physiological conditions under stress. A limitation of this study is that the model relies on simplifying assumptions without clinical validation. This research is expected to serve as a foundation for further model development by considering other regulatory factors, with implications for improving diabetes prevention and intervention strategies in stress-related conditions.