Spatial pattern analysis of A Aβ-monomer model with inflammation processes for Alzheimer’s disease Estavoyer, Maxime Torres, Nicolás Blohm, Julien Banerjee, Malay Pujo-Menjouet, Laurent Bifurcation analysis Mathematical model Turing patterns We study the emergence of spatial patterns for a system of reaction-diffusion equations, modeling the progression of Alzheimer’s disease through the interaction of Aβ-monomers, oligomers, microglial cells, and interleukins with neurons. In our work, these spatial patterns stand for inert amyloid plaques, which are extracellular deposits of Aβ-proteins and a characteristic feature of this neurodegenerative disease. Using linear analysis and numerical simulations, we show the existence of spatially heterogeneous solutions and exhibit a wide variety of possible spatially-dependent solutions: time-oscillating, low-amplitude, and high-amplitude patterns. Moreover, we carry out an extensive analysis of high-amplitude patterns in the one- and two-dimensional domains. In particular, we study the stability of branches of heterogeneous steady states through bifurcation diagrams and their selection. From this numerical bifurcation analysis, we develop some conjectures concerning the influence of inflammation and microglial cells in the formation of amyloid plaques. These findings offer insights into potential anti-inflammatory treatments that might be used to mitigate the progression of Alzheimer’s disease and the emergence of inert amyloid plaques. 2025-10-30T11:17:49Z 2025-10-30T11:17:49Z 2025-09-22 journal article Estavoyer, M., Torres, N., Blohm, J., Banerjee, M., & Pujo-Menjouet, L. (2025). Spatial pattern analysis of A Aβ-monomer model with inflammation processes for Alzheimer’s disease. Mathematical Modelling of Natural Phenomena, 20, 22. https://doi.org/10.1051/mmnp/2025022 https://hdl.handle.net/10481/107594 10.1051/mmnp/2025022 eng http://creativecommons.org/licenses/by/4.0/ open access Atribución 4.0 Internacional EDP Sciences