Mathematical Analysis of the Effect of Control on the Dynamics of Diabetes Mellitus and Its Complications
Abstract
Diabetes is a disorder in which the body becomes unable to control the amount of sugar in the blood. The pancreas (beta-cells) is not functioning normally, resulting in a partial or total lack of insulin which is the key to the mechanism converting sugar to energy. In this study, mathematical model for the dynamics of diabetes mellitus and its complications incorporating control is developed and analyzed. Positive lifestyle, which includes abstinence from alcohol, smoking and glutoning, and effective management of diabetes condition are incorporated as controls. The analytical solution of the model equations is obtained using Homotopy Perturbation Method. Numerical simulation of the model solution was done using Maple 18 Mathematical software. The parameters are varied and their effects on the model dynamics are presented graphically. The results showed that the two control measures can effectively be used to reduce the evolution of incidence of diabetes and occurrence of complications of diabetes thereby reducing the rate of morbidity and mortality due to diabetes complications.
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