Multiscale analysis of a non-periodic epidemic time series using wavelet transform

The aim of the present study was to develop a method for multiscale analysis of non-stationary and non-periodic epidemic time series. Indeed, the epidemiologists may need to know the features, at different resolutions, of short duration outbreaks that did not exhibit periodic cycles. Among of the large number of wavelets, we have developed a continuous wavelet that shows an analogous shape to the Haar wavelet, and leads to precise time localization. We applied the wavelet transform to the cholera epidemic, which began in October 2010 in Haiti. We determined the wavelet spectra of both the cholera case toll and rainfall time series, from September 01, 2010, to November 20, 2012 (812 days). The relationship between case toll and rainfall was analyzed using cross-wavelet spectra at different lags. Cholera case toll scalogram highlighted four epidemic bursts. Cross-wavelet analysis highlighted an absence of relationship between the first epidemic burst and rainfall, but a clear relationship between the following epidemic bursts and rainfall after a 3 to 8 day lag.