Modelling system of two insulin-glucose delays to achieve the dynamics of glucose changes

Due to the increased prevalence of diabetes and the irreparable complications of this disease, it is important to measure and monitor the blood glucose levels of diabetic patients. The only way to treat type 1 diabetes is monitoring insulin, and in this type of diabetes, insulin should be injected into the body in order to reduce the patient’s blood glucose as prescribed by the physician at certain times. In addition, the only way to treat type 2 diabetes is through diet and exercise daily.

We aim to use an ordinary differential equation model with two-delays to control the rate of changes in blood glucose levels throughout the day, based on the amount of food that the person consumes.

In this analytical study, we extended an ODE model which is parameterized by data collected in this study to capture dynamics of glucose and insulin. We used global sensitivity analysis method to assess model robustness with respect to parameter perturbations.

Our results have shown that utilizing the dynamics of changes in blood glucose levels throughout the day can be used to prevent hypoglycemia and hyperglycemic in the diabetic patients.

Dynamic modeling can help us to prevent hypoglycemia and hyperglycemia in the diabetic patients.