ArticleJournal of mathematical biology2014
Alzheimer's disease: analysis of a mathematical model incorporating the role of prions.
Article in Journal of mathematical biology, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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Who cites it
15 citing papers in PubMed, 61 citations in OpenAlex.
- Utilizing fractional-order operator to Alzheimer's disease dynamics.Scientific reports · 2026Article
- The role of IPFrontiers in computational neuroscience · 2025Article
- Roles of astrocytes and prions in Alzheimer's disease: insights from mathematical modeling.Journal of biological physics · 2024Article
- Personalized Computational Causal Modeling of the Alzheimer Disease Biomarker Cascade.The journal of prevention of Alzheimer's disease · 2024Article
- A scoping review of mathematical models covering Alzheimer's disease progression.Frontiers in neuroinformatics · 2024Article
- Analysis of fractal-fractional Alzheimer's disease mathematical model in sense of Caputo derivative.AIMS public health · 2024Article
- Article
- Recent Development in the Understanding of Molecular and Cellular Mechanisms Underlying the Etiopathogenesis of Alzheimer's Disease.International journal of molecular sciences · 2023Review
- A glance through the effects of CD4Computational and structural biotechnology journal · 2023Review
- A reaction-diffusion model of spatial propagation of AJournal of mathematical biology · 2021Article
- Mathematical Model Shows How Sleep May Affect Amyloid-β Fibrillization.Biophysical journal · 2020Article
- Stability analysis of a steady state of a model describing Alzheimer's disease and interactions with prion proteins.Journal of mathematical biology · 2019Article
- Article
- A physical model for dementia.Physica A · 2017Article
- Mathematical model on Alzheimer's disease.BMC systems biology · 2016Article
Corrections and comments
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Authors and funding
4 authors at 3 institutions in 3 countries.
Funding
No grant is acknowledged in the PubMed record.
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 β-amyloid plaques based on the concentrations of Aβ oligomers, PrP(C) proteins, and the Aβ-x-Aβ-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 Aβ-amyloid is constant and also when it is described by a power law.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.