Numerical Analysis of Mathematical Model for Diabetes Mellitus Disease by Using Adam-Bashfort Moulton Method

Abstract

Diabetes mellitus is a metabolic disorder characterized by elevated blood glucose levels, known as hyperglycemia. The objective of this study is to develop a mathematical model of diabetes mellitus. The model will be analyzed in terms of its equilibrium points using the Adam-Bashforth Moulton numerical method. The numerical method that used is a multistep method. The predictor step employs the Runge-Kutta method, while the corrector step uses the Adam-Bashforth Moulton method. The mathematical model of diabetes mellitus is categorized into two classes: uncomplicated diabetes mellitus and complicated diabetes mellitus. The resulting model identifies two equilibrium points: the endemic equilibrium point (complicated) and the disease-free equilibrium point (uncomplicated). The eigenvalues of these equilibrium points are positive real numbers and negative real numbers. Therefore, the stability of the system is found to be unstable and asymptotically stable, indicating that the population of individuals with uncomplicated diabetes mellitus will continue to rise, whereas the population with complications will not increase significantly over time.