Predictive modeling of a metabolism-linked cognitive neurodynamic system for Alzheimer’s disease using a radial basis scaled conjugate gradient neural network and electroencephalography-based multi-entropy analysis

Aging, metabolic syndrome, and obesity significantly increase the risk of Alzheimer’s disease (AD). This study presents a fractional-order obesity-driven AD (OD-AD) model incorporating insulin resistance and simulated using a radial basis scale conjugate gradient neural network (RB-SCG-NN). The nine-compartment model describes glucose regulation, insulin action, intestinal beta-cell function, microglial response, amyloid- β accumulation, tau aggregation, neuronal damage, and cognitive decline. Numerical solutions are obtained using the modified Atangana–Baleanu–Caputo (mABC) fractional derivative. Stability analysis, supported by a positive invariant set, confirms boundedness and long-term dynamics, while Partial Rank Correlation Coefficient (PRCC) analysis identifies the most influential parameters governing disease progression. Optimal control strategies are developed to mitigate AD progression. The proposed RB-SCG-NN model, trained on Runge–Kutta-generated datasets (70% training, 15% testing, and 15% validation), achieves high prediction accuracy with low error. Furthermore, EEG data from AD, mild cognitive impairment (MCI), and healthy individuals are analyzed using nonlinear Poincaré and entropy features with machine learning classifiers, yielding superior classification accuracy, sensitivity, and specificity. The integrated OD-AD modeling and EEG-based framework provides an effective tool for predicting, monitoring, and managing AD progression in obesity-related populations.