(untitled) (Journal of Nonlinear Modeling and Analysis, 2025)
Alzheimer’s disease (AD) is a progressive neurodegenerative disorder characterized by the accumulation of amyloid-beta (Aβ) plaques and tau neurofibrillary tangles (NFTs), as well as by chronic neuroinflammation and blood-brain barrier (BBB) dysfunction. Although these pathological features are well known, their complex interactions remain poorly understood. This study proposes a comprehensive multiscale coupled reaction-diffusion model composed of 13 partial differential equations to simulate the spatio-temporal dynamics of Aβ and tau pathology, neuroinflammatory responses, BBB integrity, and neuronal degeneration. The model captures biochemical reaction kinetics, diffusion-driven propagation, and regulatory feedback among key cellular components, including microglia, astrocytes, and cytokines. Furthermore, the effects of therapeutic interventions, such as anti-amyloid drugs and dietary modifications, are incorporated to assess their influence on disease progression. Numerical simulations using finite difference methods provide insights into how these factors contribute to or mitigate AD pathogenesis. The results support the potential of mathematical modeling as a tool to understand disease mechanisms and evaluate treatment strategies.