Spreading dynamics of an infection in a growing population

Bacteriophages spreading through populations of bacteria offer relatively simple, tuneable systems for testing mathematical models of range expansion. However, such models typically assume a static state into which to expand, which is not generally valid for bacterial-bacteriophage populations, where both the host (bacteria) and the infectious agent (bacteriophage) have similar growth rates. Here, we build on the classical FKPP theory of expanding fronts to study an infectious bacteriophage front propagating into an exponentially growing population of bacteria, focusing on the situation where the hosts are also mobile, e.g., swimming bacteria. In this case, both the infectious agent and the infected host populations take on the form of self-similar travelling waves with a fixed wave speed, as in FKPP theory, but the infected host wave also grows exponentially. Depending on the population under consideration, wave speeds are either advanced or retarded compared to the non-growing case. We identify a novel speed selection mechanism in which the shape of the bacteriophage wave controls these various wave speeds. We propose experiments to test our predictions.