Changes in Reproductive Ratio of SARS-CoV-2 Due to 1 Implementation and Rollback of Non-pharmaceutical 2 Interventions in 1,904 United States Counties

11 In response to the rapid spread of the novel coronavirus, SARS-CoV-2, the U.S. has largely delegated implementation 12 and rollback of non-pharmaceutical interventions (NPIs) to local governments on the state and county level. This 13 asynchronous response combined with the heterogeneity of the U.S. complicates quantiﬁcation of the effect of NPIs 14 on the reproductive ratio of SARS-CoV-2 on a national level. 15 We describe a data-driven approach to quantify the effect of NPIs that relies on county-level similarities to specialize 16 a Bayesian mechanistic model based on observed fatalities. Using this approach, we estimate the effect of NPIs on the 17 reproductive ratio R t in 1,904 U.S. counties incorporating implementation, subsequent rollback, and mask mandate 18 efﬁcacy. 19 We estimate that at some point before August 2, 2020, 1,808 out of the considered 1,904 U.S. counties had reduced 20 the reproductive ratio of SARS-CoV-2 to below 1.0. However, on August 2, the reproductive ration remained below 21 that threshold for only 702 counties. 22 * Corresponding author. † Equal contribution. The estimated effect of any individual NPI is different across counties. Public school closings were estimated to 23 be effective in metropolitan, urban, and suburban counties, while advisory NPIs were estimated to be effective in 24 more rural counties. The cumulative prevalence predicted by the model ranges from 0 to 58.6% across the counties 25 examined. The median is 2.6% while the 25th and 75th percentile are 1.3% and 44.6% respectively, indicating that 26 most counties are far from herd immunity. 27 Our results suggest that local conditions, including socioeconomic, demographic and infrastructural factors, in addition 28 to the cumulative prevalence are pertinent to containment and re-opening decisions. 29

: Cluster labels based on demographic and socioeconomic conditions are used to aggregate data and specialize epidemiological models. Here, one can see how cluster 1 and 3 primarily cover rural areas, while clusters 5, 2, and 4 consist of increasingly urban counties.
1-5, these are merely labels returned by the clustering algorithm without any meaning inherent to 121 the ordering. Figure 1 shows our clustering for all U.S. counties with this data available, including 122 those without any incidence of COVID-19. 123 Once we have identified the clusters, we infer the reproductive ratio of SARS-CoV-2 over time by 124 jointly optimizing the parameters of a Bayesian mechanistic model on each cluster. This process 125 is described in greater detail in Section 5. Figure 2 shows the reproductive ratio at select dates for 126 all modeled counties associated with their public transportation use. We observe that although the basic reproductive ratio of SARS-CoV-2 starts at a similar level for all 128 clusters, the speed at which counties in each cluster respond to the disease and reduce its R t differs. 129 The reproductive ratio in metropolitan counties (cluster 4), which tends to have higher reliance on 130 public transportation, decreases over the entire period. This is especially apparent going from of the virus in some areas can be seen as the reproductive ratio increases above 1 by August 2. 137 Comparisons with more features are shown in Section 4.2. From Table 2, we observe that most counties exhibited an initial reproductive ratio R 0 above 3. As 141 of August 2, however, most have successfully reduced the reproductive ratio to R t ≈ 1 after im-142 plementing NPIs. It is estimated that 17.46 to 31.83% of the population (95% confidence interval) 143 has been infected in New York, NY, which has the highest number of cases by August 2. Based on 144 the initial reproductive ratios between 2 and 4, herd immunity is reached only after 50 -70% of the 145 population has recovered, 16,17 suggesting that all U.S. counties are far from achieving herd immu-146 nity. Consequently, easing restrictions is likely to result in, and in some counties have resulted in, 147 subsequent waves of the epidemic. We state these findings for 15 representative counties in Table   148 2 and provide the same metrics for all 1,904 counties online at github.com/JieYingWu/npi-model, 149 where we also provide code and data required for reproduction. 150

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We quantify the effectiveness of NPIs for counties in each cluster, as shown in Table 3, and the 152 county-specific effectiveness of mask mandates where implemented, shown in Figure 3.   2) were estimated to have a strong response to public school closings, while rural areas (clusters 1, 157 3, and 5) responded more to national-level interventions according to our model. One surprising 158 observation is that stay-at-home orders are not given the same importance as seen in other works.

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This may be because of the concurrent estimation of its rollback effect and the mitigating effects 160 of masks in the meantime. With non-essential businesses closed, thereby limiting indoor places to 161 congregate, and masks being worn at all times, the risk of being in public spaces may remain low.

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Additionally, the effects of public school closing may confound the estimated effectiveness of stay-163 at-home orders as parents adopt stay-at-home-like practices even without mandated stay-at-home 164 orders out of necessity. were estimated to have greater effect toward reducing the reproductive ratio. Since mask mandates are implemented universally across a given state, these values are best interpreted in comparison with counties from the same state. Figure 3 shows the county-specific estimates for the effectiveness of mask mandates. Because these 166 mandates have been issued at the state level, these values tend to be similar across a given state.

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Our cluster-specialized model in particular gives rise to county-level variation for the effectiveness 168 of a single mask mandate, which may not otherwise be apparent when modeling at the state level.

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In some states, such as Texas, we observe greater effect from these mandates in urban and suburban 170 areas (clusters 2 and 4 resp.) compared to the surrounding counties. This could indicate greater 171 adherence to mask mandates, but it also likely describes the greater necessity of masks in a densely 172 populated region, where social distancing is more difficult.   spread. Naively, one may account for this heterogeneity by estimating NPI effects for each indi-194 vidual county, but this would limit analysis to counties with a large number of cases, without the 195 potential to generalize to counties with fewer cases. 196 We aim to understand the effect of each type of NPI in general, not as it depends on each individual 197 county's implementation, enforcement, or public awareness, so that this work may inform future 198 implementations in response to the outbreak of COVID-19 or another disease. Therefore, we 199 cluster counties based on variables known to affect disease spread and rely on the fundamental 200 assumption that NPI effects can be estimated for each group of counties.  Note that we exempt mask mandates from this assumption, since these appear to vary based on 202 factors unrelated to disease transmission, such as political affiliation. 15 We train a Bayesian mech-

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To generate the clustering, we partition 3,059 U.S. counties into five groups based on variables 225 which directly affect disease spread. 10 Although these are not the only factors which may affect 226 spread, they provide a meaningful basis for aggregation and separation of epidemiological data 227 and parameters.    Notably, we exclude ethnic demographics from the variables considered during clustering because 250 we assume that no direct relationship exists between race and incidence of COVID-19. We estimate the effective reproductive ratio using a semi-mechanistic Bayesian mechanistic model We describe the data collection process for NPI implementations and rollbacks in Section 5.0.1.

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Aside from mask mandates, our experiments consider n = 8 NPI types, as enumerated in Table 3.

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The model assumes a normal distribution truncated at 0 as the prior for the R 0 . For each initial reproductive ratio, we use the prior R 0,m ∼ N (3.28, κ) where κ ∼ N + (0, 0.5), in accordance with the analysis presented in Liu et al. 31 We draw the intervention weights from an offset Gamma distribution following previous work. 5 c t,m , along with the weighted probability of death, gives the number of deaths on a day for a given county as given by d t,m .
π s,m = s+0.5 τ =s−0.5 π m (τ )dτ We compare the model's expected number of deaths d t,m for region m on day t to the measured where φ ∼ N + (0, 5). To ensure that the deaths accounted for are from locally acquired infections,     Table 3. For Validation 4, which uses α i values 466 from cluster 4, we exclude L.A. county from the model fit. Additionally, we fit a "single-county" 467 model to Los Angeles County on its own, without fixing NPI effects. Figure 9 gives an overview of   Table 6: Mean error and standard deviation for fatality estimates in Los Angeles County, using the Cluster 4 model as well as validation models. Validation models are fit to L.A. county on its own, either in the same manner as described in Section 5 or as described above, with fixed NPI effects.
Those with fixed NPI effects still estimate the effect of mask mandates, as this is county-specific, and these are reported as well.     Table 3 .
One drawback of a mechanistic model is that it cannot disentangle implementations that came into 510 effect at the same time. For example, states often closed public schools at the same time as federal 511 guidelines were issued so it is difficult to discern the individual effect on reducing R t . Additionally,

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in  Table 9: Average number of days between rollbacks of interventions for all counties in the US that have implemented the two rollbacks being compared.
To further investigate the model's ability to disentangle intervention weights, we create simulated 517 trajectories of counties' deaths and cases counts based on their R 0 and the dates on which the 518 interventions came into effect. Using all counties that have more than 500 cumulative deaths on 519 August 2without super-counties, we seed each county with 200 cases in each of the first 6 days.

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The higher threshold aims to limit the disentanglement analysis to counties that have more cases 521 and are therefore likely to implement their own set of NPIs rather than follow the state timeline.

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To simulate county-specific trajectories, we construct a set of generated time series. We assign 523 intervention weights α i to be randomly generated from a Gamma distribution, the same distribution 524 as our prior on the Bayesian mechanistic model adjusted to be in the range of our learned weights.

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To reduce the complexity in disentanglement, we do not use the county-specific mask term when 526 generating the trajectories and do not fit to that term in our disentanglement model. We then 527 calculate what the R t on each day must have been based on the R 0 and the interventions in place.

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Once we have the seeded infection and the R t trajectory for each county, we can calculate daily 529 infections and thus expected fatalities. Since fewer regions are considered for disentanglement 530 runs, we fit for 1000 warmup iterations, 1800 iterations in total, and use 4 chains. Using the 531 simulated trajectories, we fit the model.  We observe that the effects of individual NPIs are not well disentangled in general. The model 534 tends to attribute more weight to few NPIs rather than spread out the weight evenly. Specifically, 535 the model tends to put more weight on stay-at-home orders. This may be because interventions 536 I 2 to I 8 are often implemented close together (see Table 8) and it is difficult to attribute effect 537 to any single one of them on a national scale. Although rollbacks are implemented with more 538 variability in time, they show similar groupings as the NPI implementation between ¿50 and ¿500 539 gatherings, and between restaurant and entertainment/gym re-openings. The region-specific mask 540 factor further entangles the rollback effects. While we can conclude that the trajectories the model 541 predicts are reliable, due to their match to measured death, and therefore the overall change in in implementation date is small. This observation seems to be in line with the similarly large 544 confidence intervals reported in previous work on varied models and regions. 2-6,8 545