Analysis of a model for the dynamics of prions II
Abstract
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.
Keywords
Cite
@article{arxiv.math/0507575,
title = {Analysis of a model for the dynamics of prions II},
author = {Hans Engler and Jan Pruess and Glenn F. Webb},
journal= {arXiv preprint arXiv:math/0507575},
year = {2007}
}