Study of fractional diabetes model with and without complication class

Abstract

This study investigates Diabetes Mellitus, focusing on global variations and complications for human health. We employ the ABC fractional derivative to develop a fractional-ordered diabetes model that incorporates complications for deeper understanding. This study is crucial for identifying patterns and trends by examining Diabetes Mellitus region-wise, aiding in targeted interventions and healthcare strategies, and using the ABC fractional derivative for a more accurate representation of the complexities associated with the disease, leading to more effective modeling and analysis. Our research yields important results that distinguish it from previous studies. Specifically, we investigate the stability and existence conditions of the proposed fractional-ordered diabetes model. Additionally, we employ the Adomian decomposition Laplace transform method to obtain solutions, enabling us to analyze the dynamics of the system comprehensively. Through graphical interpretations, we compare the recovery rates of diabetes in susceptible patients, both with and without complications. Regional analysis reveals varying prevalences and characteristics of Diabetes Mellitus, requiring tailored healthcare approaches. By incorporating complications into the fractional-ordered model, we enhance our understanding of the disease’s progression and its impact on recovery rates. These insights contribute to the broader field of diabetes research and offer valuable implications for clinical practice and public health policy.

Keywords

• Fractional diabetes model
• Atangana–Baleanu fractional derivative
• Adomian Decomposition Laplace Transform Method
• Stability analysis