Analysis of a model for the dynamics of prions II

Abstract

AbstractA new mathematical model for the dynamics of prion proliferation involving an ordinary differential equation coupled with a partial integro-differential equation is analyzed, continuing the work in [J. Prüss, L. Pujo-Menjouet, G.F. Webb, R. Zacher, Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst. 6 (2006) 225–235]. We show the well-posedness of this problem in its natural phase space Z+:=R+×L1+((x0,∞);xdx), i.e., there is a unique global semiflow on Z+ 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 in Z+; above the threshold it is unstable, and there is another unique steady state, the disease equilibrium, which inherits that property