Title: Spreading dynamics of an infection in a growing population

Abstract: Models of front propagation like the famous FKPP equation have extensive applications across scientific disciplines e.g., in the spread of infectious diseases. A common feature of such models is the existence of a static state into which to propagate, e.g., the uninfected host population. Here, we instead model an infectious front propagating into a growing host population. The infectious agent spreads via self-similar waves whereas the amplitude of the wave of infected organisms increases exponentially. Depending on the population under consideration, wave speeds are either advanced or retarded compared to the non-growing case. We identify a novel selection mechanism in which the shape of the infectious wave controls the speeds of the various waves and we propose experiments with bacteria and bacterial viruses to test our predictions. Our work reveals the complex interplay between population growth and front propagation.