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Wavelet analysis as a tool for considering non-stationarity in Epidemiology
Abstract: Epidemiological processes are typically complex and strongly not stationary. Long-term changes in climate, human demography and/or social features of human populations have generated non-stationarities in numerous epidemics. To overcome the problems of analyzing non-stationary processes different mathematical tools have been used. Wavelet decomposition is one of these tools and performs a local timescale decomposition of the time series, i.e. the estimation of its spectral characteristics as a function of time or space. Wavelet decomposition has been used for the characterization of both epidemiological and environmental time series and the relationships between these series.
After a short introduction on wavelet decomposition, the interest of the method will be illustrated by examples on Dengue epidemics in the Southeast Asia and Malaria in Africa. In these examples wavelet analysis will help us to interpret multi-scale, non-stationary time-series data and will reveal features one could not see otherwise.
Future developments around wavelet clustering, partial coherency, mutual entropy and Granger causality will be evoked as conclusion.