The interactions between the Aβ1-40 molecules species and the copper ions (Cu(II)) were intensively investigated due to their potential role in the development of the Alzheimer Disease (AD). The rate and the mechanism of the Cu(II)-Aβ complexes formation determines the aggregation pathway of the Aβ species, starting from smaller but more cytotoxic oligomers and ending up in large Aβ plaques, being the main hallmark of the AD. In our study we exploit the existing knowledge on the Cu(II)-Aβ interactions and create the theoretical model of the initial phase of the copper- driven Aβ aggregation mechanism. The model is based on the direct solution of the Chemical Master Equations, which capture the inherent stochastics of the considered system. In our work we argue that due to a strong Cu(II) affinity to Aβ and temporal accessibility of the Cu(II) ions during normal synaptic activity the aggregation driven by Cu(II) dominates the pure Aβ aggregation. We also demonstrate the dependence of the formation of different Cu(II)-Aβ complexes on the concentrations of reagents and the synaptic activity. Our findings correspond to recent experimental results and give a sound hypothesis on the AD development mechanisms.