In this talk, we consider a single species population problem with two age classes and a fixed maturation period living in a spatial transport field. A Reaction Advection Diffusion Model with time delay and nonlocal effect is derived if the mature death and diffusion rates are age independent. We discuss the existence of a travelling wave front for the special case when the birth function is the one appeared in the well-known Nicholson's blowflies equation. Furthermore, we consider and compare numerical solutions of the travelling wave fronts for the problems with nonlocal time delay effects and local time delay effects.

This is a joint work with J. Wu.