This thesis focuses on the statistical learning of digital models of neurodegenerative disease progression, especially Alzheimer's disease. It aims at reconstructing the complex and heterogeneous dynamic of evolution of the structure, the functions and the cognitive abilities of the brain, at both an average and individual level. To do so, we consider a mixed-effects model that, based on longitudinal data, namely repeated observations per subjects that present multiple modalities, in parallel recombines the individual spatiotemporal trajectories into a group-average scenario of change, and, estimates the variability of this characteristic progression which characterizes the individual trajectories. This variability results from a temporal un-alignment (in term of pace of progression and age at disease onset) along with a spatial variability that takes the form of a modification in the sequence of events that appear during the course of the disease. The different parts of the thesis are ordered in a coherent sequence: from the medical problematic, followed by the statistical model introduced to tackle the aforementioned challenge and its application to the description of the course of Alzheimer's disease, and, finally, numerical tools developed to make the previous model available to the medical community.