Mathematical Modeling of Nonlinear Vocal Biomarker Dynamics for Early Detection of Parkinson's disease Using Hybrid Ensemble Learning

Abstract

Parkinson's disease is a progressive neurodegenerative disorder characterized by motor impairment, vocal instability, and neuromuscular dysfunction affecting speech production. Early diagnosis remains clinically challenging because conventional neurological assessment and imaging procedures are often expensive, time consuming, and inaccessible in resource-limited healthcare environments. Recent advances in speech signal analysis have demonstrated that nonlinear acoustic perturbations can serve as effective biomarkers for early Parkinsonian abnormalities. However, many existing artificial intelligence-based diagnostic systems primarily emphasize predictive performance without incorporating quantitative modeling of vocal biomarker dynamics. This study presents a mathematical modeling framework for analyzing nonlinear vocal biomarker dynamics using hybrid ensemble learning for early Parkinson’s disease detection. A combined dataset consisting of 895 voice recordings and 22 clinically relevant acoustic features was utilized for experimental evaluation. The proposed framework integrates speech signal processing, statistical feature modeling, and ensemble-based machine learning to characterize disease-associated vocal perturbations. Acoustic biomarkers including jitter, shimmer, harmonic to-noise ratio (HNR), recurrence period density entropy (RPDE), and detrended fluctuation analysis (DFA) were modeled to represent instability in vocal fold dynamics. The nonlinear vocal perturbation behavior was mathematically represented as: V(t)=αJ+βS+γH+δR. where J, S, H, and Rcorrespond to jitter, shimmer, HNR, and RPDE-derived perturbation measures, respectively. To improve predictive robustness, a stacking ensemble framework integrating Random Forest, Gradient Boosting, Support Vector Machine, K-Nearest Neighbors, Logistic Regression, and Multilayer Perceptron classifiers was developed using a meta-learning strategy: y ̂ =f_m (f_1 (x),f_2 (x),...,f_n (x)) . Experimental findings demonstrated that the proposed framework achieved a classification accuracy of 97.77%, outperforming conventional standalone machine learning approaches. Statistical distribution analysis further revealed substantial nonlinear deviations in acoustic perturbation biomarkers among Parkinson’s disease patients compared with healthy individuals. The proposed framework demonstrates the potential of mathematical modeling and hybrid ensemble intelligence for developing scalable, non-invasive, and computationally interpretable diagnostic systems for early Parkinson’s disease screening and digital healthcare applications.