The study of neurodegenerative diseases represents an open challenge for modern medicine today. The aim of this thesis is to study the progression of these conditions inside the brain - in particular Alzheimer's disease - using reaction-diffusion models. The present research links the continuous diffusion model with the brain connectome, which is described by a discrete network model. Using COMSOL Multiphysics software, a three-dimensional geometry of the right brain hemisphere and its connectome structure was constructed. The study initially implemented the Fisher-Kolmogorov model to investigate the role of tau protein in initiating the disease. Subsequently, the focus shifted to the interaction between tau and β -amyloid proteins, as recent studies suggest that the spread of β-amyloid is the key driver of early cognitive decline and highly interacts with tau.