To better understand the transmission dynamics of COVID-19 in the USA, we carried out several distinct but complementary analyses, including hierarchical clustering, cross-date rank correlations, and singular value decomposition into component modes using COVID-19 case and death data from the New York Times. For our analysis we used data from 937 days of the pandemic until the end of our analysis period on August 15, 2022. Although the New York Times provides data beyond this date through early 2023, the accuracy and frequency of reporting declined during the latter part of this period. For more details on the approaches, please refer to the Methods section below.
North-south oscillations of COVID-19 using state-level data
Figure 1 provides evidence for a prominent north-south oscillating pattern of COVID-19 case rates in the United States. Figure 1A displays a hierarchical clustering dendrogram of state-by-state similarities of case rate time-series patterns for the 48 contiguous continental states. Geo-contiguous and nearby states show very similar patterns. The dendrogram also characterizes states as belonging to the main northern (purple) or the main southern (green) regional clusters, as mapped in Fig. 1B. A boundary between the north and south case rate pattern clusters lies roughly along 37–38 degrees north latitude. To extend this analysis of spatial patterns, we analyzed temporal patterns by computing a matrix that compares the rank order of the 48 continental state COVID case rates on any given date on the x-axis to the rank order of state COVID case rates on any other date on the y-axis (Fig. 1C). We refer to this matrix as cross-date state rank correlation matrix. This cross-date correlation matrix generates a structured “checkerboard” pattern. As expected, high correlations appear along the main matrix diagonal, indicating that any two or more consecutive days typically share very similar rank orderings of state case rates. However, there are unexpected results: First, this matrix displays a steady repeating pattern of block-like periods of internally high cross-date state rank correlations, all along the diagonal, with each homogeneous block pattern lasting about three months. We introduce a terminology of numbering each of these highly spatiotemporal internally correlated blocks from earliest (1) to most recent (8). National temporal wave 3 can be seen in the cross-date state rank correlation matrix as being composed of two distinct blocks, which we label 3a and 3b to retain reference to the national level temporal waves. Similarly, national temporal waves 6 can be seen to be composed of two blocks, 6a and 6b.
Second, there are at least two more diagonal bands of high correlation parallel to the main diagonal, the first at one year later (t + 1), and a second now forming at two years later (t + 2). These parallel diagonal bands result from similar state case rate rankings at almost exactly one year and two years earlier, respectively. Third, there are additional correlated sub-patterns at t + 0.5 and t + 1.5 years. For example, states have similar rankings at the intersection of waves 2 and 3b which both had high case incidences in the south. We observed that overall orderly repeating “checkerboard” pattern was transiently disrupted by the introduction of the Omicron variant of SARS-CoV-2, when all regions of the country were affected simultaneously and severely (see below). After Omicron, the regular checkerboard epidemic pattern then spontaneously restored itself, with waves 7 and 8 showing the expected state rank cross-date correlation time blocks (wave 7 correlating with waves 1 and 4, and wave 8 correlating with waves 2 and 5, respectively). Finally, we found that the relative intensity of COVID-19 cases in the northern US versus the southern US (compared to the national average) oscillates every three months, aligning well with the durations of cross-state correlation blocks in the checkerboard (Fig. 1E). This indicates that the regular block patterns in the cross-date state rank correlation matrix represent the oscillating north/south changes in case rates by latitude. Accordingly, we used the dates of these normalized incidence crossing points to define wave boundaries.
We confirmed this clear recurring pattern of case rates by creating a similar matrix of cross-date rank correlations using death rates instead of case rates (Fig. 2). The COVID-19 state death rate cross-date rank order correlation matrix generates a checkerboard pattern that is almost identical to the state case rate pattern, though not as sharp due to the lower rates of mortality compared to incidence, and with a lag of about one month compared to the timing of the case rate oscillations.
Oscillations detected by decomposition of county time series data
Given the evidence for north-south oscillations in USA COVID-19 case rates using state level data, we next sought to refine the spatiotemporal patterns of these oscillations by analyzing more granular county-level case rate time-series data. We used singular value decomposition (SVD) – a method which has extensive use in signal processing and machine learning – to decompose county-level daily case rates into lower rank fundamental components (modes).
Results of the SVD are shown in Fig. 3. The first four SVD decomposition modes accounted for more than 85% of the total USA log-transformed case rate variances by county and over time (Fig. 3A). We chose to analyze just these four modes in greater detail because after Mode IV the proportion of explained variance declined abruptly to 1%.
Figure 3B shows the four modes’ temporal patterns (eigen-trends). These patterns represent the trends of COVID-19 case rates across all counties for each day. The contribution of these trends in each county vary by a set of weights. Figure 3C shows the modes’ spatial patterns (eigen-maps) that reflect the correlation of each of the temporal patterns with each county’s observed case rate over time. Red and blue areas represent counties where the mode is strongest and white areas represent counties where the correlation is weak. For example, Mode II is strongest in the northeast (high negative correlation) and the southeast (high positive correlation) compared to the counties along the central latitude.
Modes I through IV each define a distinct spatiotemporal pattern. Mode I is the strongest (explaining 75% of the total variance) as expected because this mode captures the variance of the time-trend in case rates across all counties. The temporal trend of this mode (Fig. 3B) follows a generally cyclical annual repeating pattern with a fall-winter spike with other variable rises and falls. Modes II, III and IV capture additional local variations in the time-trend.
Figure 3D is a panel of time series heatmaps that show all individual USA county COVID case rate time series trajectories according to day (x axis), county latitude (y axis), county longitude (five columns), and mode (five rows). The first row shows the observed data, and the following rows represent the predicted case rates for each county produced by multiplying the temporal-trends (Fig. 3B) by the county specific weights underlying the spatial weights shown in Fig. 3C.
Mode I in Fig. 3D shows a vertical band-like pattern that reflects the same overall temporal wave-pattern observed in Mode I in Fig. 3B. However, the intensity of these waves vary by county because each county has its own unique weight-adjusted magnitude for this mode’s temporal trend. As expected, cases across all counties follow the average temporal trend.
Unlike Mode I, Mode II reveals a clear north-south oscillation of COVID case rates in the eastern US (East of 100 degree W). We refer to this Mode as the Eastern US Covid Oscillation; EUCO. This mode accounts for 5.2% of the total variance (Fig. 3A). In the spatial weight, this mode correlates most positively with the southeast region and negatively with the northeast region (Fig. 3C). As a result, Mode II captures a strong north/south oscillatory behavior, most prominent in the three longitudinal bands east of latitude 100W (Fig. 3D and Fig. 4A). This oscillatory behavior alternates between a high case rate in waves 1, 3a, 4, 6a and 7 in the northeast and waves 2, 3b, 5, 6b and 8 in southeast. This north-south oscillating pattern effectively locally tilts the time-invariant patterns of Mode I up and down along the axis of 37 degrees north latitude so that the waves behave as back-and-forth travelling waves across latitude.
The EUCO is further documented in Fig. 4B by plotting the daily average latitude among the counties with the highest versus the lowest case rates, among all counties east of longitude 100W. This figure reveals large semi-annual reciprocally alternating north-south latitudinal swings of the locations of the counties with the lowest and the highest case rates. Although these large oscillations were partially disrupted by the Omicron wave in winter 2022, they appear to have bounced back to their original pattern since April 2022.
Similarly, Mode III reveals a northern US COVID oscillation (NUCO). This mode explains 3.2% of the variance of the overall case rates and correlates positively with the fall waves in the northcentral US counties, and negatively correlates with winter, spring and summer waves (Figs. 3B and 3C). This mode captures high case rates in the fall (waves 3a and 6a) in longitudinal bands 90-100W and100-110W, and to a lesser degree, high cases in the winter, spring and summer in the northeast – waves 1, 2, 3b, 4, 5, 6b, 7 and 8 in longitudinal band < 80W (Fig. 3D).
Lastly, Mode IV explains 2.2% of the variance. This mode is correlated the most with the spring wave in the northeast, and to a lesser extent with case rates in the upper Midwest and southeast (Figs. 3C and 3D). Overall, this mode reflects the change in case rate severity in the first annual cycle relative to the second and third cycles (Fig. 3D).
Although Modes II-IV explain 11% of the variance compared to 75% for Mode I, most of Mode I’s captured variance occurs during the large epidemic winter peaks compared to Modes II-IV that have distinct contributions to waves in the other times of the year.
Consistent with Fig. 2, Mode II shows an alternating pattern of regional high intensity in the north and the south. When these high intensity Mode II regional patterns occur during the nadirs of Mode I, the Mode II localized epidemic is the dominant contributor to regional county case rates. This has occurred in waves 2, 4, 5, and 7. Mode III suggests that there may be an annual northeast-northcentral oscillation where case rates are highest in the northcentral region in the fall waves (3a and 6a) and highest in the northeast in the spring waves (4 and 7). Mode III was especially prominent in wave 3a. It is difficult to discern any repeating patterns of Mode IV, but this mode did have the highest intensities in waves 1 and 5.
We focused our analyses presented here on spatiotemporal patterns by latitude to generate four SVD modes. These four modes added together closely reproduce the observed case rate patterns in all five of the US regions analyzed (Fig. 5).
Note that these oscillatory patterns in COVID peak rates generate travelling epidemic waves. In Fig. 5, as shown for example for the observed cases in the longitudinal band B (80–90W), the sequential waves 3a and 3b move gradually from north to south over time, while wave 5 travels from the south to the north. Wave 6a begins in the north and moves southward, but the near-simultaneous nationwide emergence of Omicron obscures the expected 6b component of the travelling wave.
In addition to these patterns across latitudes, we also found limited but less-striking evidence of additional spatial structure by longitude within latitudinal bands.