  A new mathematical model for the dynamics of prion proliferation involving an
ordinary differential equation coupled with a partial integro-differential
equation is analyzed, continuing earlier work. We show the well-posedness of
this problem in a natural phase space, i.e. there is a unique global semiflow
in the phase space associated to the problem.
  A theorem of threshold type is derived for this model which is typical for
mathematical epidemics. If a certain combination of kinetic parameters is below
or at the threshold, there is a unique steady state, the disease-free
equilibrium, which is globally asymptotically stable; above the threshold it is
unstable, and there is another unique steady state, the disease equilibrium,
which inherits that property.
