In this presentation we introduce a model accouting for the in vivo dynamics of Alzheimer's disease including the role of the prion protein onto memory impairment in the disease. We use a size-structured equation to describe the formation of \beta amyloid plaques coupled with three differential equations on the concentration of A\beta-oligomers, PrP^C proteins (prion) and A\beta-\times-PrP^C complex since this latter has been considered, in some recent findings, to be responsible for the synaptic toxicity. We prove well-posedness of the problem and stability results of the unique equilibrium, when the polymerization rate of \beta-amyloid is constant and then it is described as power law.

Finally, we discuss about possible implications of this model in drug design and an experimental validation.