A Multiscale Coupled Reaction-Diffusion Model of Amyloid-Beta and Tau Pathology in Alzheimer’s Disease (Journal of Nonlinear Modeling and Analysis, 2025)
Alzheimer’s disease (AD) is a progressive neurodegenerative disorder characterized by the accumulation of amyloid-beta $({\rm A}β)$ plaques and tauneurofibrillary tangles (NFTs), as well as by chronic neuroinflammation andblood-brain barrier (BBB) dysfunction. Although these pathological featuresare well known, their complex interactions remain poorly understood. Thisstudy proposes a comprehensive multiscale coupled reaction-diffusion modelcomposed of 13 partial differential equations to simulate the spatio-temporaldynamics of ${\rm A}β$ and tau pathology, neuroinflammatory responses, BBB integrity, and neuronal degeneration. The model captures biochemical reactionkinetics, 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 anddietary modifications, are incorporated to assess their influence on diseaseprogression. Numerical simulations using finite difference methods provide insights into how these factors contribute to or mitigate AD pathogenesis. Theresults support the potential of mathematical modeling as a tool to understanddisease mechanisms and evaluate treatment strategies.