Engler, Hans; Prüss, Jan; Webb, Glenn F. Analysis of a model for the dynamics of prions. II. (English) Zbl 1103.92024 J. Math. Anal. Appl. 324, No. 1, 98-117 (2006). Summary: 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 part I by J. Prüss, L. Pujo-Menjouet, G. F. Webb and R. Zacher [Discrete Contin. Dyn. Syst., Ser. B 6, No. 1, 225–235 (2006; Zbl 1088.92043)]. We show the well-posedness of this problem in its natural phase space \(Z_+: =\mathbb{R}_+\times L_1^+((x_0,\infty);xdx)\), 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. Cited in 2 ReviewsCited in 28 Documents MSC: 92C50 Medical applications (general) 45K05 Integro-partial differential equations 47N60 Applications of operator theory in chemistry and life sciences 47D03 Groups and semigroups of linear operators 92C60 Medical epidemiology Keywords:viral-host interaction: stability; evolution equations; proliferation Citations:Zbl 1088.92043 PDFBibTeX XMLCite \textit{H. Engler} et al., J. Math. Anal. Appl. 324, No. 1, 98--117 (2006; Zbl 1103.92024) Full Text: DOI arXiv References: [1] Arendt, W.; Batty, C.; Hieber, M.; Neubrander, F., Vector-Valued Laplace Transforms and Cauchy Problems, Monogr. Math. (2001), Birkhäuser: Birkhäuser Basel · Zbl 0978.34001 [3] Eigen, M., Prionics or the kinetic basis of prion diseases, Biophys. Chem., 63, 11-18 (1996) [4] Masel, J.; Jansen, V. A.A.; Nowak, M. A., Quantifying the kinetic parameters of prion replication, Biophys. Chem., 77, 139-152 (1999) [5] Nowak, M. A.; Krakauer, D. C.; Klug, A.; May, R. M., Prion infection dynamics, Integrative Biology, 1, 3-15 (1998) [6] May, R. M.; Nowak, M. A., Virus Dynamics. Mathematical Principles of Immunology and Virology (2000), Oxford Univ. Press: Oxford Univ. Press Oxford · Zbl 1101.92028 [7] Prüss, J.; Pujo-Menjouet, L.; Webb, G. F.; Zacher, R., Analysis of a model for the dynamics of prions, Discrete Contin. Dyn. Syst., 6, 225-235 (2006) · Zbl 1088.92043 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.