Abstract : The SIR system is a reaction-diffusion model that describes the spread of diseases in a population. In this talk, we present a multi-species version of this model, describing the interactions between the propagation of different strains of a disease. The model takes the form of a system of coupled reaction-diffusion PDEs. We shall study the long-time behavior of solutions (convergence to equilibria, speed of convergence…) and prove that there is a « selection via propagation » phenomenon.