Modelling the progression of Degenerative Diseases (DD) is essential for detection, prevention, and treatment, yet it remains challenging due to the heterogeneity in disease trajectories among individuals. Factors such as demographics, genetic conditions, and lifestyle contribute to diverse phenotypical manifestations, necessitating patient stratification based on these variations. Recent methods like Subtype and Stage Inference (SuStaIn) have advanced unsupervised stratification of disease trajectories, but they face potential limitations in robustness, interpretability, and temporal granularity. To address these challenges, we introduce Disease Progression Modelling and Stratification (DP-MoSt), a novel probabilistic method that optimises clusters of continuous trajectories over a long-term disease time-axis while estimating the confidence of trajectory sub-types for each biomarker. We validate DP-MoSt using both synthetic and real-world data from the Parkinson's Progression Markers Initiative (PPMI). Our results demonstrate that DP-MoSt effectively identifies both sub-trajectories and subpopulations, and is a promising alternative to current state-of-the-art models.