A novel fractional Parkinson's disease onset model involving α-syn neuronal transportation and aggregation: A treatise on machine predictive networks

Artificial intelligence plays a crucial role in medical care by enhancing diagnostic accuracy, personalizing treatment plans, and streamlining administrative processes, ultimately improving patient outcomes and operational efficiency. Additionally, it aids in predictive analytics, helping to identify potential health issues before they become critical. This paper presents a novel fractional mathematical model for α-syn transport and aggregation in neurons leading to the onset of Parkinson's disease (α-syn-TAN-OPD). A Nonlinear Autoregressive Exogenous (input) Neural Network optimized with Levenberg Marquardt Backpropagation technique (NARX-NN-LMBT) is expertly deployed on the fractional α-syn-TAN-OPD model. Fractional Adams-Bashforth-Moulton numerical scheme is deployed to generate three scenarios with five different fractional order cases each by varying α-syn synthesis rate, monomeric α-syn concentration decay, and misfolded α-syn production rate. These synthetic datasets are passed to the NARX-NN-LMBT to simulate, model, and anticipate the α-syn-TAN-OPD scenarios. The NARX-NN-LMBT technique is validated using mean squared error (MSE), root MSE, normalized MSE and mean absolute error performance evaluations. Graphical descriptions of regression indices, error-input cross correlation, error autocorrelation, error histograms further detail the prowess of the NARX-NN-LMBT technique for the accurate modeling of α-syn-TAN-OPD cases. A comparative analysis is drawn between the numerical scheme and the NARX-NN-LMBT with mean absolute error lying between the ranges of 10−7 to 10−8. NARX-NN-LMBT forecasting ability is assessed on single and multiple steps with the MSE lying in the range of 10−13 to 10−16.