January  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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