La Trobe Mathematics Colloquium: Complex demodulation of epidemiological time series data
by Prof Bob Anderssen, Data61 CSIRO Canberra
Abstract: Understanding how seasonal patterns change from year to year is important for the management of infectious disease epidemics. Here, a mathematical formalization of the application of complex demodulation is proposed and analysed, which has previously only been applied in an exploratory manner in the context of infectious diseases. This method extracts the changing amplitude and phase from seasonal data, allowing comparisons between the size and timing of yearly epidemics. The method is validated using synthetic data in order to displays how it recovers the key features within epidemic data. In particular, both annual and biennial synthetic data are analysed, and the effect of delayed epidemics on the extracted amplitude and phase is explored. The usefulness of complex demodulation is demonstrated using national notification data for influenza in Australia. This method clearly highlights the higher number of notifications and the early peak of the influenza pandemic in 2009. It is also established that epidemics that peaked later than usual generally followed larger epidemics and involved fewer overall notifications. The proposed procedure and its analysis establishes a role for complex demodulation in the study of seasonal epidemiological events.
For More Information: This talk is based on collaborative research with Alexandra Hogan, NCEPH, ANU, and Imperial College, London, and Katie Glass, NCEPH, ANU, and some of their colleagues; in particular, the ANZIAM Journal paper by Hogan, Glass and Anderssen (doi:10.1017/S1446181116000377).