Epidemiological modeling includes handling disease transmission data that originated from various processes influencing the given disease transmission. The nature of these data is highly diverse, not perfectly reliable, and they are complex with respect to the underlying data generation process. The more complex the data are, the less the application of classical statistical methods can be used for analysis to reveal critical information that is hidden. This study focuses on introducing mathematical tools that are powerful in analyzing time-dependent disease transmission data specifically related to dengue outbreaks. These dengue cases are processed with respect to external variables in a local context to identify any time-dependent relationships.

The fast Fourier transformation (FFT) method is useful in identification of the periodic pattern of the epidemiological data and climate variations. However, providing the spectral properties through FFT is lacking; therefore we investigated the usability wavelet theory to analyze dengue cases with respect to external variations such as climate and human mobility. Since FFT is not capable of identifying the statistical relationship between two spectra, the cross wavelet and wavelet coherence methods were applied to investigate the correlations and phase differences among two time series.

Dengue cases and climate data from 2008 to 2015 in Colombo, Jakarta, and Thailand were analyzed applying FFT. Reported weekly dengue incidences, rainfall, and temperature data for an identical time span of eleven years from 2006 were used from the Municipal Council (CMC) area and then analyzed using wavelet theory to identify any spectral patters in time. Both FFT and wavelet analysis were performed using structured computer algorithms, and the case studies demonstrated the applicability of these tools in capturing critical spectral information hidden in multivariate time series data.