Some Results on the Mathematical Modeling of Alzheimer’s Disease

In this presentation, we discuss recent results in the mathematical modeling of Alzheimer’s disease, based on the amyloid cascade hypothesis related to the polymerization process of the Aβ protein. We first present the analytical and numerical study of a spatial model describing the propagation of Aβ in interaction with neuronal activity. We then discuss a second model that incorporates the immune response, in particular the inflammation mediated by microglial cells. Finally, we present qualitative results related to the estimation of the nucleation rate, a critical parameter in the progression of the disease, for which no experimental measurements are currently available.