  In this Note we study a mathematical model for the progression of Alzheimer's
Disease in the human brain. The novelty of our approach consists in the
representation of the brain as two superposed graphs where toxic proteins
diffuse, the connectivity graph which represents the neural network, and the
proximity graph which takes into account the extracellular space. Toxic
proteins such as beta-amyloid and tau play in fact a crucial role in the
development of Alzheimer's disease and, separately, have been targets of
medical treatments. Recent biomedical literature stresses the potential impact
of the synergetic action of these proteins. We numerically test various
modelling hypotheses which confirm the relevance of this synergy.
