Mathematical model for drug therapy in patients with diabetes mellitus.

Abstract

Diabetes Mellit us is a chronic illness that requires continuing medical care and ongoing patient self-management. education and support. to prevent acute complications and to reduce the risk of long-term complications. Diabetes Mellitus care is complex and requires that many issues, beyond glycemic control, he addressed. A large body of eviclence exists from American Diabetes Association on diagnostic, classificar ion and scrccninp; that supports a. r:tn�c of intervention- to improve Diabetes l\lcllit11s outcomes. So far the models developed for blood glucose regulatory system (BGRS) during drug therapy in patients with Diabetes mellitus are based on glucose and insulin only. This study presents a new Mathematical Model for Drug 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 + f(t) and whose solution was analyzed to provide the systems natural frequency, w0, which is the basic descriptor or saturat.ion level of the drug. It was established that the resonance period for the final model, that is, T0 = 3.76912 hrs, is in the arccpt.able t herapem ic ra11ge and agrees well with r.he data fort.he existing insulin therapy. Bv ,•111plt1_,•i11g I ill' nu><IPL ii i, shown I hnr . t lw peak. which is t.he t inu- period for insulin to he most 1,ffect.ivl: in lowcruu; bloor! suu,n . i:::; shorter than T;1 = 5.3199 hrs. fur i.hc existing model. This IIHHl,,J would help t lw medical prar t it ionr-rs to predict clrng t.hcrapv in patients with Diabetes �lellit11s. in such a wav that the conceutrarion ofthe drug remains in r.he therapeut.ic range.