We propose a rather simple model, which fits well the weekly human influenza incidence data from England and Wales. A standard way to analyse seasonally varying time-series is to decompose them into different components. The residuals obtained after eliminating these components often do not reveal time dependency and are normally distributed. We suggest that conclusions should not be drawn only on the basis of residuals and that one should consider the analysis of squared residuals. We show that squared residuals can reveal the presence of the remaining seasonal variation, which is not exhibited by the analysis of residuals, and that the modelling of such seasonal variations undoubtedly improves model fit.