Time-dependent spectral analysis of epidemiological time-series with wavelets

Abstract

In the current context of global infectious disease risks, a better understanding of the dynamics of major epidemics is urgently needed. Time-series analysis has appeared as an interesting approach to explore the dynamics of numerous diseases. Classical time-series methods can only be used for stationary time-series (in which the statistical properties do not vary with time). However, epidemiological time-series are typically noisy, complex and strongly non-stationary. Given this specific nature, wavelet analysis appears particularly attractive because it is well suited to the analysis of non-stationary signals. Here, we review the basic properties of the wavelet approach as an appropriate and elegant method for time-series analysis in epidemiological studies. The wavelet decomposition offers several advantages that are discussed in this paper based on epidemiological examples. In particular, the wavelet approach permits analysis of transient relationships between two signals and is especially suitable for gradual change in force by exogenous variables.

On spatially explicit models of cholera epidemics

“…Time-series analysis of cholera cases in endemic regions such as Bangladesh shows a time variability with subannual, annual and interannual components. The low-frequency variability has been linked to long-term climatic oscillations (Pascual et al 2000;Koelle et al 2005;Cazelles et al 2007), and the overall seasonality has been found to experience competing effects with two routes of transmissions: one enhanced by increasing rainfall and the other buffered by increasing water pools (Ruiz-Moreno et al 2007).…”

Estimation of reproduction number and non stationary spectral analysis of dengue epidemic

“…Cross comparison of two different time series in time and frequency, can be done through cross wavelet and wavelet coherence analysis. Here we give a brief overview of the wavelet analysis for epidemiological time series closely following [8] and our analysis for Dengue time series.…”

“…A closer examination of these relationships needs Wavelet Coherence, discussed in next section. The wavelet coherence C x,y (a, τ ) is the cross-spectrum smoothened over time and scale (expectation value) and normalized by the smoothened spectrum of each time series [34,8]. It allows to explain the causality and coherence between the signals.…”

“…Wavelet based techniques are ideally suited for non stationary signals (time series), as they can capture both the time and periodicity in a single domain [27]. Wavelet based methods have recently been used extensively in epidemiological studies [20,23,6,26] including Dengue and its association with El-nino oscillation [9] (see [8] for review). Through Wavelet spectral analysis, we analyzed the duration of post monsoon Dengue incidences in Ahmedabad and found significant temporal variations every year.…”

A century of transitions in New York City's measles dynamics

“…Figure 5 displays the normalized NYC measles time series again, but in two different ways that highlight the changes in frequency structure that we seek to understand. The top panel of figure 5 shows weekly normalized measles on a square root scale, suppressing [36][37][38][39][40], which reveals the dominant frequencies at each point in time.…”