Inflammation processes in Alzheimer disease modeling

In this talk we are interested in the mathematical modeling of the progression of Alzheimer disease. Alzheimer is a neurodegenerative disease which is known to be associated with the misconformation, aggregation and propagation of different proteins in the neural system. The proteins Aβ-monomers are identified to be relevant in the early stages of development of the disease. Unfortunately, the precise mechanisms of aggregation and diffusion of the Aβ-monomers are not well known. In this presentation, we state a mathematical model describing the reactions involving Aβ-monomers, its aggregation forms, microglial cells and interleukins in order to study the progression of Alzheimer’s disease. Analysis of the existence of steady states depending on the parameters will be discussed and numerical simulations is provided in order to observe the possible dynamics of solutions and their asymptotic stability. This presentation is taken from a work done with Ionel Ciuperca, Laurent Pujo-Menjouet, Nicolas Torres and Vitaly Volpert.