title: Alzheimer's disease: analysis of a mathematical model incorporating the role of prions.
abstract: We introduce a mathematical model of the in vivo progression of Alzheimer's disease with focus on the role of prions in memory impairment. Our model consists of differential equations that describe the dynamic formation of β-amyloid plaques based on the concentrations of Aβ oligomers, PrP(C) proteins, and the Aβ-x-Aβ-PrP(C)complex, which are hypothesized to be responsible for synaptic toxicity. We prove the well-posedness of the model and provided stability results for its unique equilibrium, when the polymerization rate of Aβ-amyloid is constant and also when it is described by a power law.
authors.affiliation: Département de Mathématique, Faculté des Sciences, Université Djillali Liabes, 22000 , Sidi Bel Abbès, Algeria, mhelal_abbes@yahoo.fr.
authors.forename: Mohamed
authors.initials: M
authors.lastname: Helal
authors.forename: Erwan
authors.initials: E
authors.lastname: Hingant
authors.forename: Laurent
authors.initials: L
authors.lastname: Pujo-Menjouet
authors.forename: Glenn F
authors.initials: GF
authors.lastname: Webb
mesh_terms: D000544:Alzheimer Disease / Q000378:metabolism*; D016229:Amyloid beta-Peptides / Q000378:metabolism*; D006801:Humans; D008954:Models, Biological; D011328:Prions / Q000378:metabolism*
chemical_list: D016229:Amyloid beta-Peptides; D011328:Prions