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

TL;DR

This paper presents a mathematical model for Alzheimer's disease progression emphasizing prions' role, using differential equations to describe amyloid plaque formation and analyzing the model's stability and well-posedness.

Contribution

It introduces a novel differential equation model incorporating prion dynamics in Alzheimer's disease, with mathematical analysis of stability and well-posedness.

Findings

Model proves well-posedness and stability under certain conditions.

Provides a mathematical framework linking prions to amyloid plaque formation.

Analyzes the impact of polymerization rates on disease dynamics.

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.