Abstract: In this paper, the existence of a travelling wave solution for a single population model with spatio-temporal delay is investigated by employing singular perturbation. The theoretical results are validated by using a numerical method. When the time delay is very small, a wave front solution exists; however, as the time delay increases, the shape of this travelling wave solution can vary and an oscillation wake can occur.

Key words: spatio-temporal delay, travelling wave solution, singular perturbation method