Finding the causative pathophysiological mechanisms for Parkinson's disease (PD) is important for developing therapeutic interventions. Until recently, it was believed that Lewy bodies (LBs), the hallmark of PD, are mostly composed of alpha-synuclein (α-syn) fibrils. Recent results (Shahmoradian et al., Lewy pathology in Parkinson's disease consists of crowded organelles and lipid membranes, Nature Neuroscience 22 (2019) 1099-1109) demonstrated that the fibrillar form of α-syn is lacking from LBs. Here we propose that this surprising observation can be explained by the catalytic activity of the fibrillar form of α-syn. We assumed that α-syn fibrils catalyze the formation of LBs, but do not become part of them. We developed a mathematical model based on this hypothesis. By using the developed model, we investigated the consequences of this hypothesis. In particular, the model suggests that the long incubation time of PD can be explained by a two-step aggregation process that leads to its development: (i) aggregation of monomeric α-syn into α-syn oligomers and fibrils and (ii) clustering of membrane-bound organelles, which may cause disruption of axonal trafficking and lead to neuron starvation and death. The model shows that decreasing the rate of destruction of α-syn aggregates in somatic lysosomes accelerates the formation of LBs. Another consequence of the model is the prediction that removing α-syn aggregates from the brain after the aggregation of membrane-bound organelles into LBs has started may not stop the progression of PD because LB formation is an autocatalytic process; hence, the formation of LBs will be catalyzed by aggregates of membrane-bound organelles even in the absence of α-syn aggregates. The performed sensitivity study made it possible to establish the hierarchy of model parameters with respect to their effect on the formation of vesicle aggregates in the soma.