Design of fractional innate immune response to nonlinear Parkinson's disease model with therapeutic intervention: Intelligent machine predictive exogenous networks

In this study, a novel application of intelligent machine predictive exogenous neuro-structure optimized with the Levenberg-Marquardt (IMPENS-LM) algorithm is presented to analyze the dynamics of fractional innate immune response to nonlinear Parkinson's disease propagation considering the impact of therapeutic interventions (PDP-TI). A novel design of the fractional PDP-TI model is constructed with a nonlinear system of five differential compartments representing healthy neurons and infected neurons, extracellular α-syn, and both active and resting microglia. The presented IMPENS is formulated with neuro-structure of nonlinear autoregressive exogenous neural networks with efficient backpropagation of LM algorithm to solve the scenarios of nonlinear fractional PDP-TI model by varying neuron infection rate, survival percentage of α-syn from the death of infected neurons, the density of microglia, infected neurons death rate due to α-syn aggregations, and the ratio of therapeutic approach targeting α-syn with fixed values of annihilation rate of activated microglia, apoptosis rate of neurons and microglia etc. The IMPENS-LM algorithm is operated on synthetic datasets of fractional PDP-TI system generated through the Grunwald-Letnikov fractional finite difference-based numerical computing paradigm for each variant. The sufficient large numerical experimentation is performed with the IMPENS-LM technique to analyze the behavior of the dynamics of the PDP-TI model with the help of different proximity, complexity, and statistical measures in terms of MSE-based iterative fitness learning arcs, absolute error analysis, error autocorrelation plots, and error histograms, to substantiate the efficacy of stochastic solver on sundry fractional orders.