Almost a year and a half after the first case of the disease caused by the novel coronavirus SARS-CoV2 was recorded in the United States, the country has reported over 42 million cases, over 680,000 deaths, 88 million initial unemployment claims filed from March 21, 2020, to the present, and an estimated 30,000 additional deaths attributable to pandemic-related unemployment [1,2]. Additionally, up to 30% of COVID-19 survivors and some asymptomatic individuals may be subject to sequalae including a deterioration in health-related quality of life that may last 9 months or longer [3-6]. Despite the unprecedented pandemic, the US government has not implemented national COVID-19 restrictions, instead leaving it to states and metropolitan areas to determine what public health measures are appropriate in their context, based on unclear guidelines [7-12]. This has led to a patchwork of measures and sometimes diverging national, state, and local guidance [7-9]. Additionally, unclear and divergent public health recommendations, among other factors, have likely affected public acceptance of measures such as social distancing, face masking, and crowd avoidance [13-15]. For example, despite the evidence that masks help prevent the spread of the virus, on March 6, protestors held a mask-burning rally on the steps of the Idaho state capitol [16], the first conviction in a plot to kidnap Michigan Governor Whitmer for imposing a mask mandate was handed down in August of 2021 [17], and Florida Governor DeSantis’s ban of local mask mandates has been subject to court challenges and likely appeals [18].

After enduring shutdowns for most of the 2020-21 winter, most US metropolitan areas began reopening in early- to mid-March, 2021 [16,19,20], despite contrary guidance and concerns of explosive growth after reopening [21,22]. Reopening is at least chronologically associated with public desensitization to COVID-19 news and lack of compliance with health guidance [23]. Since June 2021, the emergence of the delta variant has led to a global third wave of COVID-19 cases including in the Unites States, with 98.4% of new cases in the Unites States comprising lineage B.1.617.2 [24]. There is significant concern that reopening has led to an upsurge and possibly explosive growth in the pandemic, especially as new variants spread across the country, and if either health policy or social acceptance of policy reduces or eliminates social distancing. The ramifications of the Delta and other variants for the reemergence of explosive growth under reopening conditions and with limited vaccination are unclear [25]. Thus, it is imperative to have timely and objective surveillance at local levels to inform public health decisions, including metrics such as the 7-day persistence rate that inform questions around where on the epidemiological curve the pandemic currently lies—whether it is in the state of explosive growth, peaking and declining, or that it is peaking with a plateau [26,27]. A large 7-day persistence value is indicative of explosive growth.

This report provides surveillance data relevant to the question of whether the pandemic is exploding, peaking, or plateauing for the 25 largest US metropolitan areas. Specifically, it provides weekly data for the 6 weeks ending on September 19, 2021, on the novel metrics of speed, acceleration, and jerk, and the 7-day persistence effect. This captures information relevant to the determination of a possible peak and reversal in the most recent Delta-fueled wave of COVID-19 in the United States.

We calculated the speed, acceleration, jerk, and 7-day persistence rate by applying dynamic panel data modeling and additional methods introduced by [7,26]. These methods have been previously applied globally at the country level [26-31] and in the United States at the state level [28] and comprise the basis for the Global SARS-CoV-2 Surveillance Project [32]. This paper updates the findings by Oehmke et al [27], who previously applied these methods to US metropolitan areas.

The metrics used in the paper are speed, acceleration, jerk, and persistence. Speed is the number of new metropolitan area cases per day per 100,000 population and is a measure of how fast the pandemic is growing from day to day. To address differences in reporting across different days of the week, we calculate speed (and other indicators) on a weekly basis for 7-day ISO (International Organization for Standardization) weeks [33]. Acceleration is the week-over-week change in weekly average speed and is the primary indication of whether the pandemic is getting worse (positive acceleration) or better (negative acceleration or deceleration) from week to week. Jerk is the change in acceleration. A positive jerk signifies increasing acceleration—not only is the pandemic getting worse, but it is getting worse more rapidly this week than last. A large positive jerk can be associated with super-spreading events, emergence of a new variant, policy shift, or other change that affects the underlying infection rates. A negative jerk indicates a declining acceleration possibly including a shift from positive to negative acceleration, and if associated with a policy shift, may indicate policy success. The 7-day persistence rate is the number of cases per 100,000 today that are statistically attributable to cases 7 days ago. A positive 7-day persistence rate can signify the presence of linked super-spreader events, the emergence of a new variant, or continued policy ineffectiveness. During the first year of the pandemic, persistence was associated with mega-spreader events (eg, when on a weekend people were infected at a sports event, religious gathering, political rally, etc, they go to another event the next weekend and infect more people, who then go to another event, leading to a persistent “echo forward” effect of the original infection [27]). Mathematically, persistence case numbers that are close to or exceeding 100% of total cases lead to rapid or explosive growth in the number of cases. A small positive persistence may indicate a diminishing pandemic. A negative number indicates that the high number of cases last week is associated with a lower number of cases this week, suggesting that the high number of cases was an aberration rather than an indication of a persistent issue in the metropolis. A negative 7-day persistence rate is indicative of a slowing pandemic, whether via a natural progression or through public health control measures.

We collected data from USAFacts for the week of 2021 ending August 1, 2021, through the week ending September 19, 2021. Using the US Census Bureau definitions of metropolitan area, we determined the various counties comprising the 25 largest US metropolitan areas and collected data on the total (cumulative) number of COVID-19 cases in each county for each day. We preprocessed the data only by creating a variable containing the number of new cases per county per day to show the change in the cumulative case count from the prior day to that day (first difference). We used data from the first 2 weeks, ie, the weeks ending August 1, 2021, and August 8, 2021, to create lagged values used in the analysis, resulting in a sample period of 6 weeks from the week ending August 15, 2021, to the week ending September 19, 2021, for which we had a complete data set. We analyzed the data using STATA/MP, version 17.0 (Stata Corp LLC); the dynamic panel data modeling is accomplished using STATA’s “xtabond” procedure. We report the weekly average speed, acceleration, jerk, and 7-day persistence effect for the most recent 6 weeks of 2021. The results for the prior weeks of 2021 are available from the authors upon request.

We also report the vaccination rates in California and Florida, which are useful in interpreting the results. Vaccination data are taken from the USAFacts website. Multimedia Appendix 1 contains additional methodological detail.

Table 1 reports the population-weighted average results for the 25 metropolitan areas. Speed increased from 34.03 cases per day per 100,000 persons during the week ending August 15, 2021, to a peak of 36.84 during the week ending September 5, 2021, before declining to 29.01 for the week ending September 19, 2021. Acceleration started at a positive 3.96, then declined and turned negative during the weeks ending September 12, 2021, and September 19, 2021. Jerk was negative for the first 5 weeks of the period, before turning positive during the week ending September 19, 2021. The positive jerk coupled with a negative acceleration (deceleration) means that the deceleration is slowing, which is potentially indicative of a slow decline or upcoming plateau in the number of cases. Persistence started at 1.67 new cases per day per 100,000 that were statistically attributable to cases from the prior week, during the week ending August 15, 2021. Persistence increased to a peak of 2.22 the week ending August 29, 2021, before declining to a value of 1.06 the week ending September 19, 2021.

Disaggregating the results by metropolitan area reveals a variety of patterns over the 6 weeks. We present an illustrative selection of these patterns graphically; complete results in tabular form are available in Multimedia Appendix 2 [34-38].

Figure 1 shows illustrative temporal patterns for speed. The population-weighted average showed a slight increase in speed through the week ending September 5, 2021, then a slight decrease. Chicago followed the national pattern of a slight increase over the first 3 or 4 weeks of the sample period, and then a slight decrease in speed. Other cities following this pattern include New York, Houston, Atlanta, Philadelphia, Phoenix, Boston, San Francisco, Riverside, Orlando, Tampa, Seattle, San Diego, and Portland. Miami started off the sample period at its peak with a high rate of speed, which declined significantly over the sample period especially in the last 2 weeks; Tampa and Orlando followed the national pattern of peaking in mid-August but had significant decreases in speed over the last 2 weeks, similarly to Miami. Los Angeles also saw a significant decline in speed over the period, but from a lower starting point. San Francisco and San Diego, while mirroring the national peak, declined rapidly in the end of the sample period to significantly decrease their speed, with San Francisco and San Diego reaching single-digit speeds. San Antonio experienced a small decrease in speed over the sample period. Dallas, Washington DC, Detroit, Minneapolis, Baltimore, Charlotte, St. Louis, and Portland saw slightly increasing speed over the period.

Figure 2 shows illustrative temporal patterns for acceleration. The population-weighted average acceleration started slightly positive and ended slightly negative. Chicago’s acceleration mirrored this pattern before ending at essentially zero for the week ending September 19, 2021. Other cities following this pattern include New York, Houston, Atlanta, Philadelphia, Phoenix, Boston, San Francisco, Riverside, Orlando, Tampa, Seattle, San Diego, and Portland. Miami started with positive acceleration, but then began a rapid deceleration (negative acceleration) that is reflected in a still declining number of cases. Los Angeles, San Francisco, Orlando, Tampa, San Diego, Atlanta, and Riverside also ended the sample period with large decelerations, although the deceleration in San Francisco and the other California areas occurred primarily in the last 2 weeks of the sample period. Dallas, Washington DC, Detroit, Minneapolis, Baltimore, St. Louis, Charlotte, and Portland had some amount of fluctuation in acceleration, but ended the period with small positive accelerations.

Figure 3 shows illustrative temporal patterns for jerk—the change in acceleration. The population-weighted average jerk changes little over the sample period: it is very slightly negative the week ending August 15, 2021, and very slightly positive the week ending September 19, 2021. Since acceleration was negative (deceleration) that week, the positive jerk means that the speed is still decreasing but less rapidly. In other words, the latest wave of the pandemic has peaked, but at a national level, it is not decreasing rapidly. Chicago follows almost exactly the population-weighted average. New York, Boston, Detroit, Seattle, Minneapolis, Denver, and Baltimore were mostly similar. St. Louis inverted the average pattern, starting with small negative jerk, moving into a positive jerk, but ending the sample period with a small negative jerk. Dallas, Houston, Washington DC., Philadelphia, Phoenix, Charlotte, San Antonio, and Portland showed large fluctuations in jerk. Miami had negative jerk for the weeks ending August 15, 2021, through September 5, 2021, but jerk turned positive for the weeks ending September 12, 2021, and September 19, 2021. Los Angeles, Atlanta, San Francisco, Riverside, San Diego, Tampa, and Orlando moved from positive or near-zero jerk to large negative jerk.

Figure 4 shows illustrative temporal patterns for persistence, the number of daily new cases statistically attributable to new cases 7 days previously.

The metropolitan average persistence started out at 1.7 new cases per day per 100,000 statistically attributable to new cases 7 days prior, peaked at 2.2 the week ending August 29, 2021, and then declined at 1.1 the week ending September 19, 2021. As a percentage of speed, metro average persistence peaked at 6.0% the week ending August 29, 2021, and then declined to 3.7% the week ending September 19, 2021. Of the 25 largest metropolitan areas, 22 (88%) followed a similar pattern.

Exceptions to the pattern were Washington DC, Charlotte, and St. Louis. Charlotte had a definite peak the week ending September 5, 2021, and a decline the following 2 weeks, ending the sample period with a slightly higher persistence than at the start. Washington DC was similar to Charlotte but with lower numbers and a muted peak. St. Louis had a relatively high and flat persistence rate. As a percentage of total new cases, St. Louis had values from 20% to 26% over the sample period, which was notably higher than most other cities.

Table 2 provides comparisons across the 25 largest US metropolitan areas for the week ending September 19, 2021. We report the surveillance metrics of speed, acceleration, jerk, and persistence for each metropolitan area, ranked by speed. Charlotte, NC has the fastest speed at 73 new cases per day per 100,000 population, positive acceleration and jerk, and the second-highest persistence at 6.94 new cases the week ending September 19, 2021 (meaning that 6.94 new cases per day are statistically attributable to new cases in the prior week). Tampa, Orlando, and Miami have negative acceleration, consistent with their falling numbers of new cases over the entire sample period. St. Louis has the highest persistence at 7.01, meaning that over 21% of new cases during the week ending September 12, 2021, were statistically attributable to new cases the prior week. This is nearly 6 times the population-weighted average rate of 3.6%. At the bottom of the table, Riverside, San Diego, Los Angeles, and San Francisco all had single-digit speed and negative acceleration, jerk, and persistence.

The correlation coefficient between the prior week’s persistence number and the current week’s speed is 0.577 (P<.001).

For additional context in interpreting these results, we present vaccination rate data from California and Florida in Figure 5. Both California and Florida saw the number of new vaccinations per day peak in mid-April and decline through the end of July. Both states had a smaller “second wave” of vaccinations that began about mid-August.