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arXiv · 1302.7013

Alzheimer's disease: analysis of a mathematical model incorporating the role of prions

Mohamed Helal·Erwan Hingant·Laurent Pujo-Menjouet·Glenn F. Webb
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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 {\beta}-amyloid plaques based on the concentrations of A{\beta} oligomers, PrPC proteins, and the A{\beta}-x-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 {\beta}-amyloid is constant and also when it is described by a power law.

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Mohamed Helal, Erwan Hingant, Laurent Pujo-Menjouet, Glenn F. Webb. 2013-02-27. Alzheimer's disease: analysis of a mathematical model incorporating the role of prions. https://doi.org/10.1007/s00285-013-0732-0

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