Understanding strong Allee effects in diffusive population models with a Stefan-type moving boundary

We examine travelling wave solutions of a reaction–diffusion equation that incorporates a strong Allee effect in the population growth term and a Stefan-like moving boundary condition governing the advance of the population front. These two mechanisms, which have been examined separately in other model frameworks, have not previously been analysed together. We investigate the sharp-fronted travelling wave solutions that arise using both direct numerical simulation and travelling wave analysis, enabling us to obtain the relationship between the wave speed and the parameter associated with the moving boundary condition. Our results show that this model admits sharp-front travelling waves with wave speed c<c∗, where c∗ is a critical speed that depends on the Allee threshold. This highlights a distinction between our model and the classical population models, which admit travelling wave solutions over R with speed c≥c∗. We also present a systematic method for determining c∗ for particular choices of strong Allee population growth models. To complement the numerical simulations in the limiting regimes, we employ asymptotic analysis for the cases c→0+ and c→c∗−, enabling us to construct sharp-front travelling wave solutions.