Diffusion versus network models as descriptions for the spread of prion diseases in the brain

In this paper we will discuss different modeling approaches for the spread of prion diseases in the brain. Firstly, we will compare reaction–diffusion models with models of epidemic diseases on networks. The solutions of the resulting reaction–diffusion equations exhibit traveling wave behavior on a one-dimensional domain, and the wave speed can be estimated. The models can be tested for diffusion-driven (Turing) instability, which could present a possible mechanism for the formation of plaques. We also show that the reaction–diffusion systems are capable of reproducing experimental data on prion spread in the mouse visual system. Secondly, we study classical epidemic models on networks, and use these models to study the influence of the network topology on the disease progression.