Correlation analysis of the dispersion of SARS-CoV-2 in Mexico

Abstract

In this paper, we propose a method to analyze correlations in pandemic-related data across different geographical regions, relying on the analysis of correlations for non-stationary time series, which are typical of pandemic data. Unlike traditional epidemiological approaches focused on medical and modeling perspectives during a pandemic, our method emphasizes post-pandemic analysis to assess how societal responses; such as lockdowns, travel restrictions, mobility patterns, and vaccination campaigns, manifest in the collective behavior of regions. These insights can inform future public health strategies and enhance understanding of the complex dynamics underlying pandemic spread and control.

Figures (6)

• Figure 1: Peak filtration: The figure displays the effect of the notch filter on the time series on the states of Ciudad de México (top left panels), Jalisco (top right panels), Nuevo León (bottom left panels), and Puebla (bottom right panels). For each state, the first row shows the raw daily new case counts and its power spectrum, while the second row shows the filtered time series and its corresponding power spectrum. In all cases, the first column depicts the new daily cases (top) and the filtered time series (bottom), while the second column shows the power spectrum before (top) and after (bottom) filtering.
• Figure 2: Returns time series: The figure displays the returns time series for the states of Ciudad de México (top left panels), Jalisco (top right panels), Nuevo León (bottom left panels), and Puebla (bottom right panels). In the figures, the green curves in the inset panels show the returns time series of the corresponding filtered data, while the black curves show the original filtered time series for comparison.
• Figure 3: Correlation matrices of daily new infections across the 32 Mexican states at selected times during the pandemic ($t=80, 288, 400, 480, 544, 880, 960$ days). The matrices highlight the temporal evolution of inter-state correlations, including periods of strong nationwide synchronization and others characterized by block structures reflecting regional heterogeneity.
• Figure 4: Centroids and representative correlation matrices of the four clusters identified by $k$-means analysis. Panel (a) shows the correlation matrices emerging at times $t= 128, 224, 480, 784$ days (inward perspective), together with the centroid of Cluster 1 ($C_1$) (flat perspective) which is characterized by weak correlations, with a predominance of near-zero values and some small positive correlations. Panel (b) shows the correlation matrices emerging at times $t= 704, 816, 864, 912$ days (inward perspective) together with the centroid of Cluster 2 ($C_2$) (flat perspective) which shows intermediate correlation patterns, suggesting coordinated but heterogeneous adjustments across states. Panel (c) shows the correlation matrices emerging at times $t= 384, 432, 608, 656$ days (inward perspective), together with the centroid of Cluster 3 ($C_3$) (flat perspective) which shows intermediate correlation patterns, suggesting coordinated but heterogeneous adjustments across states. Panel (d) shows the correlation matrices emerging at times $t= 176, 272, 352, 544$ days (inward perspective), together with the centroid of Cluster 4 ($C_4$) (flat perspective) which shows strong, nearly uniform correlations across all states.
• Figure 5: Symbolic dynamics of the clusters, aligned with nationwide incidence data and major vaccination milestones. The transitions between clusters highlight shifts in the collective behavior of states across different pandemic phases.