Abstract
Alzheimer's disease (AD) is characterized by the accumulation of amyloid beta, which is strongly associated with disease progression and cognitive decline. Despite the approval of monoclonal antibodies targeting Aβ, optimizing treatment strategies while minimizing side effects remains a challenge. This study develops a mathematical framework to model Aβ aggregation dynamics, capturing the transition from monomers to higher-order aggregates, including protofibrils, toxic oligomers, and fibrils, using mass-action kinetics and coarse-grained modeling. Parameter estimation, sensitivity analysis, and data-driven calibration ensure model robustness. An optimal control framework is introduced to identify the optimal dose of the drug as a control function that reduces toxic oligomers and fibrils while minimizing adverse effects, such as amyloid-related imaging abnormalities (ARIA). The results indicate that Donanemab achieves the most significant reduction in fibrils. These findings provide a quantitative basis for optimizing AD treatments, providing valuable insight into the balance between therapeutic efficacy and safety.