A mathematical model for the dynamics of prion
proliferation is analyzed. The model involves a system of three
ordinary differential equations for the normal prion forms, the
abnormal prion forms, and polymers comprised of the abnormal forms.
The model is a special case of a more general model, which is also
applicable to other models of
infectious diseases. A theorem of threshold type is
derived for this general model. It is proved that below and at the threshold,
there is a unique steady state, the disease-free equilibrium, which is
globally asymptotically stable. Above the threshold, the disease-free
equilibrium is unstable, and there is another steady state,
the disease equilibrium, which is globally asymptotically stable.
Mathematics Subject Classification: 92D25, 92C60.