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 de-scribe the dynamic formation of β-amyloid plaques based on the concentrations of Aβ oligomers, PrPC proteins, and the Aβ-×-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 β-amyloid is constant and also when it is described by a power law. CONTENT