The goal of this work is the modelling of the propagation of BSE (Bovine Spongiform Encephalopathy) at the scale of a very large population (Great-Britain) in order to predict its extinction time and to evaluate the efficiency of the main feedban regulation. To this end, we first elaborated a multitype branching process in discrete time with age and population dependent individual transitions. The types are the health states at each age. Then, assuming that the disease is rare at the initial time, and assuming that the probability for an animal to be exposed to a given infective is inversely proportional to the total population size, we derived from this model, as the initial size of the population increases to ∞, a limit process on the incidence of clinical cases. This limit process may be either considered as a singletype d-Markovian process with a Poissonian transition distribution, or a multitype Bienaymé–Galton–Watson process having d types corresponding to the memory of the process. We studied the behavior of the limit process and estimated its unknown parameters using a Bayesian approach.