Alzheimer’s disease: analysis of a mathematical model incorporating the role of prions. (English) Zbl 1307.35305
Authors’ 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, PrP\(^C\) proteins, and the A\(\beta\)-\(\times\)-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 \(\beta \)-amyloid is constant and also when it is described by a power law.
Reviewer: Anthony D. Osborne (Keele)
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 92C50 | Medical applications (general) |
| 35B35 | Stability in context of PDEs |
| 35F61 | Initial-boundary value problems for systems of nonlinear first-order PDEs |
| 92B05 | General biology and biomathematics |
| 34L30 | Nonlinear ordinary differential operators |
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