Prions are infectious proteins that, when misfolded, propagate their abnormal structure and cause degenerative diseases in humans and other mammals. The infectious units of prion diseases are aggregates of misfolded proteins, which grow by recruiting normal proteins (conversion) and break down into smaller aggregates (fragmentation).

We introduce a stochastic model describing the dynamics of a population of prion aggregates. The model is formulated as a continuous-time Markov chain that tracks both the number of aggregates and the total number of misfolded protein monomers within aggregates. We derive and solve a PDE for their joint probability generating function, establish results on population growth and mean aggregate size, and analyze how model parameters influence aggregate population dynamics.