Intelligent exogenous predictive networks for nonlinear Parkinson's disease model involving delay with effects of immunotherapy.

Artificial intelligence is used to simulate, solve, or approximate the dynamics of complex neurodegenerative diseases through accurate prediction. Parkinson's disease (PD) is a progressive disorder caused by the loss of dopaminergic neurons, leading to motor impairments such as muscle stiffness, tremors, and Bradykinesia. In this study, artificial intelligence-driven nonlinear autoregressive exogenous neural networks (AI-NARX-NN) are applied to the existing mathematical model reflecting the dynamics of innate as well as adaptive immune responses to PD under immunotherapy (IAIR-PDI). The IAIR-PDI model is characterized by a delay differential system of five classes representing the densities of healthy neurons, affected neurons, extracellular alpha-syn, activated microglia, and activated T cells. The performance of the AI-NARX-NN is investigated in scenarios of active immunization, passive immunization, and no treatment in the IAIR-PDI model. In the active immunization case, short antigenic peptide vaccination is given to the patients that mimics alpha-syn to generate antibodies, whereas in the passive immunization case, antibody vaccination is given directly to PD patients. The simulation results, including mean-square-error-based convergence curves, histograms, error correlation, solution plots, and corresponding absolute errors, confirm strong agreement between the AI-NARX-NN predictions and the reference numerical solutions, supporting the accuracy of the proposed scheme for the IAIR-PDI model with different time delays.