2005/07/27 by Hans Engler, Engler, Hans, Jan Pruess +3
Biochemistry, Genetics and Molecular Biology · Mathematics · Medicine · #35Q80 #92C45 #Amino Acid Enzymes and Metabolism #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models #Prion Diseases and Protein Misfolding #math.AP #msc:35Q80 #msc:92C45
paper · pdf · doi:10.48550/arxiv.math/0507575
arxiv created 2005/07/27 · openalex publication_date 2005/07/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.