Abstract
Alzheimer's disease (AD) is caused by the build-up of amyloid beta (A$\beta$) proteins in the brain, leading to memory loss and cognitive decline. Despite the approval of monoclonal antibodies targeting A$\beta$, optimizing treatment strategies while minimizing side effects remains a challenge. This study develops a mathematical framework to model A$\beta$ 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.