Mathematical modeling of insulin therapy in patients with diabetes mellitus

Abstract

This study presents a Mathematical Model Insulin Therapy in Patients with Diabetes Mellitus which includes external rate at which blood glucose, insulin and epinephrine are being increased in the form, (Y=AY+r ⃗(t)) ̇ andwhose solution was analyzed to provide the systems natural frequency, ω_o which is the basic descriptor of saturation level of the drug. It was established that the resonance period for the final model, that is, T0=3.76912 hrs, is in the acceptable therapeutic range and agrees well with the data for the existing insulin therapy. By employing the model, it is shown that, the peak, which is the time period for insulin to be most effective in lowering blood sugar, is shorter than T0= 5.3199 hrs, for the existing model. This model would help the medical practitioners to predict drug therapy in patients with Diabetes Mellitus, in such a way that the concentration of the drug remains in the therapeutic range.