Previous models of disease spread involving delay have used basic SIR (susceptible - infectious - recovery) formulae and approaches. This paper demonstrates how time-varying SEIRS (S - exposed -I -R -S) models can be extended with delay to produce wave propagations that simulate periodic wave fronts of disease spread in the context of population movements. The model also takes into account the natural mortality associated with the disease spread. Understanding the delay of an infectious disease is critical when attempting to predict where and how fast the disease will propagate. We use cellular automata to model the delay and its effect on the spread of infectious diseases where population movement occurs. We illustrate an approach using wavelet transform analysis to understand the impact of the delay on the spread of infectious diseases. The results indicate that including delay provides novel ways to understand the effects of migration and population movement on disease spread.