In this contribution, nonlinear constitutive equations are suggested and analyzed for both self-diffusion and cross-diffusion. In particular, the modelling of cross-diffusion is reconsidered by starting from a basic SIR model, which is extended by either a discrete or continuous spatial distribution. Comparing the discrete model with patches to the continuous PDE model prepares the way for a micro-macro transition, where the continuous model can be deduced from the discrete. This deduction allows us to advance in the development of epidemic models with cross-diffusion. This is further elaborated in the complete version of the paper.