Alzheimer's disease: analysis of a mathematical model incorporating the role of prions
From MaRDI portal
Publication:471079
DOI10.1007/s00285-013-0732-0zbMath1307.35305arXiv1302.7013OpenAlexW2019289857WikidataQ50876344 ScholiaQ50876344MaRDI QIDQ471079
Laurent Pujo-Menjouet, Erwan Hingant, Glenn F. Webb, Helal, Mohamed Atef
Publication date: 13 November 2014
Published in: Journal of Mathematical Biology (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1302.7013
Stability in context of PDEs (35B35) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Medical applications (general) (92C50) Nonlinear ordinary differential operators (34L30) General biology and biomathematics (92B05) Initial-boundary value problems for systems of nonlinear first-order PDEs (35F61)
Related Items
A physical model for dementia, From a microscopic to a macroscopic model for Alzheimer disease: two-scale homogenization of the Smoluchowski equation in perforated domains, Bifurcation Analysis and Finite-Time Contraction Stability of an Alzheimer Disease Model, Mathematical model of Alzheimer's disease with prion proteins interactions and treatment, A reaction-diffusion model of spatial propagation of A\(\beta\) oligomers in early stage Alzheimer's disease, The work of Glenn F. Webb, Microscopic and macroscopic models for the onset and progression of Alzheimer's disease, Finite-time stability and optimal control of a stochastic reaction-diffusion model for Alzheimer's disease with impulse and time-varying delay, Stability analysis of a steady state of a model describing Alzheimer's disease and interactions with prion proteins, Well-Posedness of a Mathematical Model for Alzheimer's Disease, A dual-gradient chemotaxis system modeling the spontaneous aggregation of microglia in Alzheimer’s disease, A mathematical model demonstrating the role of interstitial fluid flow on the clearance and accumulation of amyloid \(\beta\) in the brain, Analysis and Numerical Simulations of a Reaction-Diffusion Model with Fixed Active Bodies, Analysis and numerical simulation of a polymerization model with possible agglomeration process, A continuous-time mathematical model and discrete approximations for the aggregation of β-Amyloid, The amyloid cascade hypothesis and Alzheimer’s disease: A mathematical model
Cites Work
- Unnamed Item
- Unnamed Item
- A mathematical model of the impact of novel treatments on the A\(\beta\) burden in the Alzheimer's brain, CSF and plasma
- The shape of the polymerization rate in the prion equation
- On the solvability of a mathematical model for prion proliferation
- An in vivo intermediate filament assembly model
- Size distribution dependence of prion aggregates infectivity
- A mathematical analysis of the dynamics of prion proliferation
- Analysis of a model for the dynamics of prions
- Well-posedness for a model of prion proliferation dynamics
- On solutions of the Lifshitz-Slyozov model
- Prion dynamics with size dependency–strain phenomena
- Effects of General Incidence and Polymer Joining on Nucleated Polymerization in a Model of Prion Proliferation
