Many neurodegenerative diseases are connected to the spreading of misfolded prionic proteins. In this talk, we introduce and analyze a positivity-preserving numerical method for the discretization of the Fisher-Kolmogorov equation, modelling accumulation and spreading of both $\alpha$-synuclein and Amyloid-$\beta$, related to Parkinson’s and Alzheimer's diseases, respectively. The proposed approximation method couples the Discontinuous Galerkin (DG) method on polygonal/polyhedral grids for space discretization, with the $\theta$-method for time integration. We show that the proposed approach is structure-preserving, in the sense that it guarantees that the discrete solution is non-negative, a feature that is of paramount importance in practical applications. Several numerical tests will be shown, including simulations of the $\alpha$-synuclein spreading in a two-dimensional brain slice and the Amyloid-$\beta$ spreading in a patient-specific setting by using a three-dimensional geometry.