  We consider a model for the polymerization (fragmentation) process involved
in infectious prion self-replication and study both its dynamics and non-zero
steady state. We address several issues. Firstly, we give conditions leading to
size repartitions of PrPsc aggregates that exhibit bimodal distributions, as
indicated by recent experimental studies of prion aggregates distribution.
Secondly, we show stability results for this steady state for general
coefficients where reduction to a system of differential equations is not
possible. We use a duality method based on recent ideas developed for
population models. These results underline the potential influence of the
amyloid precursor production rate in promoting amyloidogenic diseases. Finally,
we numerically investigate the influence of different parameters of the model
on PrPsc accumulation kinetics, in the aim to study specific features of prion
strains.
