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

Mohammad AlShurbaji, Lamis Abdul Kader, Hadia Hannan, Maruf Mortula and Ghaleb A. Husseini ()
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Mohammad AlShurbaji: Biomedical Engineering Graduate Program, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
Lamis Abdul Kader: Biomedical Engineering Graduate Program, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
Hadia Hannan: Biomedical Engineering Graduate Program, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
Maruf Mortula: Department of Civil Engineering, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates
Ghaleb A. Husseini: Department of Chemical and Biological Engineering, American University of Sharjah, Sharjah P.O. Box 26666, United Arab Emirates

IJERPH, 2023, vol. 20, issue 2, 1-23

Abstract: 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.

Keywords: diabetes mellitus; diabetes prevalence; diabetes complications; diabetes control; ODEs; numerical methods; mathematical model; stability analysis (search for similar items in EconPapers)
JEL-codes: I I1 I3 Q Q5 (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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