Stability Analysis of the Improved Analytic Solution of the Mathematical Model for the Complications of Diabetes Mellitus

Diabetes mellitus has become a global silent epidemic rising at an alarming rate throughout the world due to increase in life expectancy, obesity and sedentary lifestyles. It is a chronic disease that can lead to complications over time. These complications can be prevented or minimized with the support of government, private sectors and medical expertise. This paper proposed an improvement in the existing mathematical model based on number of diabetics with complications and number of diabetics with and without complications. Stability of the proposed model is analyzed and observed that the complications can be controlled during diabetes persists. Analytic solution of the system of ordinary differential equation is achieved. In this paper, the proposed model precise the understanding of diabetes, its complications and how it can be controlled. The stability analysis of the model showed that the models were stable asymptotically at various parameter values. The model showed that the rate at which complications are controlled is very important parameter in controlling the diabetes and its complications. If the value of the rate at which complications are controlled is high, then the number of diabetics with complications is decreased. Numerical solution of the proposed models were obtained using Euler method. Numerical simulations of the analytic solutions were obtained at various values of the parameters.