Preprint 2013-06
Mohamed Helal, Erwan Hingant, Laurent Pujo-Menjouet, Glenn Webb:
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 _-amyloid plaques based on the concentrations of A_ oligomers, PrPC proteins, and the A_-_-PrPC 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 _-amyloid is constant and also when it is described by a power law.
This preprint gave rise to the following definitive publication(s):
Mohamed HELAL, Erwan HINGANT, Laurent PUJO-MENJOUET, Glenn WEBB: Alzheimers disease: analysis of a mathematical model incorporating the role of prions. Journal of Mathematical Biology, vol. 69, 5, pp. 1207-1235, (2014).