A Neural Network-Based Scheme for Nonlinear Fractional Malaria Disease Model Using Spectral Method

This study presents a numerical approach for solving a fractional-order malaria model incorporating vaccination and infected immigrants. The model is analyzed using the spectral collocation method and Levenberg–Marquardt neural networks (LMNNs). The LMNN framework, employing fifteen neurons with a log-sigmoid transfer function, is trained through supervised learning with an 80%–15%–5% data split for training, validation, and testing. Model accuracy is assessed using correlation analysis, histogram curves, regression plots, and function fitness evaluations. Additionally, a dynamic and stability analysis is performed via the basic reproduction number (Formula presented.). Results highlight that increasing vaccination coverage significantly reduces malaria transmission, especially in the absence of infected immigrants. Furthermore, the vaccination rate is optimized using particle swarm optimization (PSO), demonstrating rapid convergence and adaptability. All graphical results are generated using Matlab and Python.