The accumulation of amyloid-beta (A \(\beta \) ) plays a critical role in Alzheimer’s Disease progression. We present a mathematical framework using stochastic Smoluchowski-type models to investigate the aggregation and degradation dynamics of A \(\beta \) in the brain. The framework allows us to capture the evolution of monomers, dimers, and higher-order polymers, emphasizing their interplay under physiological and pathological conditions. To mitigate the pathological effects of A \(\beta \) aggregation, we formulate an optimal control problem incorporating control inputs designed to reduce dimer and polymer densities. The objective function minimizes polymer density over the treatment period and dimer density at the final time, reflecting immediate and long-term therapeutic goals. Numerical simulations explore the effects of key parameters on A \(\beta \) dynamics, including clearance rates, weight factors, and control input limits. Our results demonstrate the effectiveness of optimal control strategies in reducing pathological aggregates while preserving system stability.