Mathematical Modeling of Oxidative Stress in Alzheimer’s Disease: A Differential Equations Approach

Alzheimer’s disease (AD) develops as a progressive dementia condition through the step-by-step breakdown of nerve cells. Neurodegeneration in this context primarily results from metal ions, including copper, iron, zinc, and aluminum, building up in the system. The aggregation of amyloid-beta (Aβ) peptides and oxidative stress generation stem from metal ion involvement acting as defining characteristics of Alzheimer’s disease pathology. We developed a comprehensive mathematical model based on 24 coupled ordinary differential equations (ODEs) to represent the interactions between metal ions, Aβ peptides, reactive oxygen species (ROS), antioxidant defenses, and tau protein phosphorylation. The mathematical model monitors how metal ion concentrations change over time and examines their competitive binding effects, which trigger a series of reactions, resulting in oxidative stress and subsequent tau protein damage. The model uses analytical and numerical mathematical methods to expose nonlinear behaviors and threshold effects while offering mechanistic insights into the course of disease development. This model functions as a quantitative framework for assessing how therapeutic interventions that target metal dyshomeostasis and oxidative stress can potentially affect outcomes.