A wavelet time-frequency analysis of pandemic dynamics and impacts — COVID-19 case study

This paper subscribes to the whole framework of mathematical approaches applied to real-life phenomena, especially epidemiology. The objective of this project is to provide a quantitative computational method for understanding the phenomenon of pandemics. The paper applies a time-frequency modeling of the dynamics of pandemic spread, especially the last COVID-19 using wavelets as a toolkit. The wavelet model shows a well-fit to the multiphases of the time dependence of the pandemic spread on the number of cumulative infected individuals and the velocity of spread. The study showed the performance of wavelet modeling in extracting characteristics of the pandemic dynamics such as the number of multiphases and/or waves. In many existing studies, this number is fixed arbitrarily in advance and the model used is adapted accordingly. The study showed that the wavelet toolkit permits one to fix such a number optimally. The study is experimented on different cases from different continents during the period between February 2020 and December 2022. Measures of closeness are provided to show the accuracy, the efficiency and the performance of the model. Spectrogram analysis and statistical measures are applied for these purposes, such as a normalized average quadratic error depending on the wavelet decomposition, and an accuracy prediction quotient for the percentage of correctly detected multi-waves. We also applied an absolute deviation error to localize the predicted residues and finally, the well-known Jackknife test for the number of the peaks predicted. Among the conclusions of this study, we notice the relationship of the pandemic with the economic and political situation of the communities. The need to diversify sources of income is mentioned to maintain a certain level of stability and services during pandemics. This conclusion was evident in countries such as Tunisia and Turkey, where tourism is a major tributary in their economies, which forced them to open borders at the beginning of the emergence of stability or decrease with the impact of the pandemic and the number of infections, resulting in the emergence of a new wave exceeding quietly all the pivotal moments in the sample.