Analysis of a model for the dynamics of prions

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.