# American Institute of Mathematical Sciences

2006, 6(1): 225-235. doi: 10.3934/dcdsb.2006.6.225

## Analysis of a model for the dynamics of prions

 1 Fachbereich Mathematik und Informatik, Martin-Luther-Universität Halle-Wittenberg, D-06120 Halle, Germany, Germany 2 Department of Mathematics, Vanderbilt University, Nashville, Tennessee TN 37240, United States 3 Department of Mathematics, Vanderbilt University, Nashville, TN 37340

Received  May 2005 Revised  October 2005 Published  October 2005

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.
Citation: Jan Prüss, Laurent Pujo-Menjouet, G.F. Webb, Rico Zacher. Analysis of a model for the dynamics of prions. Discrete & Continuous Dynamical Systems - B, 2006, 6 (1) : 225-235. doi: 10.3934/dcdsb.2006.6.225
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