A reaction-diffusion model for a single species with age structure. I Travelling wavefronts on unbounded domains

In this paper, we derive the equation for a single species population with two age classes and a fixed maturation period living in a spatially unbounded environment. We show that if the mature death and diffusion rates are age independent, then the total mature population is governed by a reaction-diffusion equation with time delay and non-local effect. We also consider the existence, uniqueness and positivity of solution to the initial-value problem for this type of equation. Moreover, we establish the existence of a travelling-wave front for the special case when the birth function is the one which appears in the well-known Nicholson's blowflies equation and we consider the dependence of the minimal wave speed on the mobility of the immature population.