Comprehensive Study of a Diabetes Mellitus Mathematical Model Using Numerical Methods with Stability and Parametric Analysis

Diabetes is sweeping the world as a silent epidemic, posing a growing threat to public health. Modeling diabetes is an effective method to monitor the increasing prevalence of diabetes and develop cost-effective strategies that control the incidence of diabetes and its complications. This paper focuses on a mathematical model known as the diabetes complication (DC) model. The DC model is analyzed using different numerical methods to monitor the diabetic population over time. This is by analyzing the model using five different numerical methods. Furthermore, the effect of the time step size and the various parameters affecting the diabetic situation is examined. The DC model is dependent on some parameters whose values play a vital role in the convergence of the model. Thus, parametric analysis was implemented and later discussed in this paper. Essentially, the Runge-Kutta (RK) method provides the highest accuracy. Moreover, Adam-Moulton's method also provides good results. Ultimately, a comprehensive understanding of the development of diabetes complications after diagnosis is provided in this paper. The results can be used to understand how to improve the overall public health of a country, as governments ought to develop effective strategic initiatives for the screening and treatment of diabetes.

Automated summary

Diabetes is a global silent epidemic that poses a growing threat to public health. This paper focuses on a mathematical model called the diabetes complication (DC) model, using various numerical methods to analyze and monitor the diabetic population over time. The model's parameters and convergence are discussed, with the Runge-Kutta method providing the highest accuracy. The results provide a comprehensive understanding of diabetes complications and can be utilized to improve overall public health through effective strategies for screening and treatment.