Parkinson's disease is a progressive neurodegenerative disorder characterized by accumulation of abnormal isoforms of alpha-synuclein. Alpha-synuclein is proposed to act as a prion in Parkinson's disease: In its misfolded pathologic state, it favors the misfolding of normal alpha-synuclein molecules, spreads trans-neuronally, and causes neuronal damage as it accumulates. This theory remains controversial. We have previously developed a Susceptible-Infected-Removed (SIR) computational model that simulates the templating, propagation, and toxicity of alpha-synuclein molecules in the brain. In this study, we test this model with longitudinal MRI collected over 4 years from the Parkinson's Progression Markers Initiative (1,068 T1 MRI scans, 790 Parkinson's disease scans, and 278 matched control scans). We find that brain deformation progresses in subcortical and cortical regions. The SIR model recapitulates the spatiotemporal distribution of brain atrophy observed in Parkinson's disease. We show that connectome topology and geometry significantly contribute to model fit. We also show that the spatial expression of two genes implicated in alpha-synuclein synthesis and clearance, SNCA and GBA, also influences the atrophy pattern. We conclude that the progression of atrophy in Parkinson's disease is consistent with the prion-like hypothesis and that the SIR model is a promising tool to investigate multifactorial neurodegenerative diseases over time.