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In this Note we study a mathematical model for the progression of Alzheimer'sDisease in the human brain. The novelty of our approach consists in therepresentation of the brain as two superposed graphs where toxic proteinsdiffuse, the connectivity graph which represents the neural network, and theproximity graph which takes into account the extracellular space. Toxicproteins such as beta-amyloid and tau play in fact a crucial role in thedevelopment of Alzheimer's disease and, separately, have been targets ofmedical treatments. Recent biomedical literature stresses the potential impactof the synergetic action of these proteins. We numerically test variousmodelling hypotheses which confirm the relevance of this synergy.

The role of beta-amyloid and tau proteins in Alzheimer's disease: a mathematical model on graph