Abstract:
Alzheimer’s disease (AD) is a progressive neurodegenerative disorder characterized by complex biochemical and cellular interactions that evolve overlong time scales. In this study, we develop a novel fractional order mathematical model of AD using the Caputo derivative, which enables the explicit representation of long term memory and hereditary effects features that are essential for accurately capturing the slow cumulative nature of neuro degeneration. The proposed model incorporates the dynamics of neurons, amyloid beta (Aß) aggregates, tau protein tangles, and microglial responses, thus providing a comprehensive framework for simulating the intricate pathological mechanisms underlying disease progression. A detailed sensitivity analysis is conducted to determine the relative influence of each pathological factor, revealing amyloid toxicity as the dominant driver of neuronal loss and emphasizing its critical role in AD pathophysiology. To address potential intervention strategies, we formulate an optimal control problem that adaptively regulates preventive and therapeutic measures over time, aiming to minimize neuronal damage while balancing treatment costs. To complement the analytical approach, a Physics Informed Neural Network (PINN) is developed to learn the system dynamics directly from noisy or incomplete data while enforcing biological and physical constraints derived from the model equations. Comparative experiments demonstrate that the PINN achieves superior predictive accuracy and robustness relative to conventional neural networks, particularly under data scarcity, by leveraging embedded domain knowledge. By uniting fractional calculus, optimal control theory, and physics-informed machine learning, this work not only advances the computational modeling of Alzheimer’s disease but also offers practical insights into optimizing therapeutic interventions. The integrated methodology has the potential to support clinical decision making and guide the design of effective, personalized treatment strategies.
Page(s):
172-172
DOI:
DOI not available
Published:
Journal: 4th International Conference of Sciences “Revamped Scientific Outlook of 21st Century, 2025” , November 12,2025, Volume: 1, Issue: 1, Year: 2025
Keywords:
machine learning
,
Alzheimers disease
,
Fractional Calculus
,
Optimal Control
,
physics informed neural networks