key: cord-0791683-5co38iqn
authors: Noland, Robert B.
title: Mobility and the effective reproduction rate of COVID-19
date: 2021-01-28
journal: J Transp Health
DOI: 10.1016/j.jth.2021.101016
sha: 824c0a2e67727fa738e1c85712b85df990e33ebb
doc_id: 791683
cord_uid: 5co38iqn

OBJECTIVES: Due to the infectiousness of COVID-19, the mobility of individuals has sharply decreased, both in response to government policy and self-protection. This analysis seeks to understand how mobility reductions reduce the spread of the coronavirus (SAR-CoV-2), using readily available data sources. METHODS: Mobility data from Google is correlated with estimates of the effective reproduction rate, R(t), which is a measure of viral infectiousness (Google, 2020). The Google mobility data provides estimates of reductions in mobility, for six types of trips and activities. R(t) for US states are downloaded from an on-line platform that derives daily estimates based on data from the Covid Tracking Project (Wissel et al., 2020; Systrom et al., 2020). Fixed effects models are estimated relating mean R(t) and 80% upper level credible interval estimates to changes in mobility and a time-trend value and with both 7-day and 14-day lags. RESULTS: All mobility variables are correlated with median R(t) and the upper level credible interval of R(t). Staying at home is effective at reducing R(t,). Time spent at parks has a small positive effect, while other activities all have larger positive effects. The time trend is negative suggesting increases in self-protective behavior. Predictions suggest that returning to baseline levels of activity for retail, transit, and workplaces, will increase R(t) above 1.0, but not for other activities. Mobility reductions of about 20–40% are needed to achieve an R(t) below 1.0 (for the upper level 80% credible interval) and even larger reductions to achieve an R(t) below 0.7. CONCLUSIONS: Policy makers need to be cautious with encouraging return to normal mobility behavior, especially returns to workplaces, transit, and retail locations. Activity at parks appears to not increase R(t) as much. This research also demonstrates the value of using on-line data sources to conduct rapid policy-relevant analysis of emerging issues.

Mobility data from Google is correlated with estimates of the effective reproduction rate, R t , which is a 10 measure of viral infectiousness (Google, 2020) . The Google mobility data provides estimates of 11 reductions in mobility, for six types of trips and activities. R t for US states are downloaded from an on-12

line platform that derives daily estimates based on data from the Covid Tracking Project (Wissel et al., 13 2020, Systrom et al., 2020) . Fixed effects models are estimated relating mean R t and 80% upper level 14 credible interval estimates to changes in mobility and a time-trend value and with both 7-day and 14-15 day lags. 16

Results 17

All mobility variables are correlated with median R t and the upper level credible interval of R t . Staying at 18

home is effective at reducing R t, . Time spent at parks has a small positive effect, while other activities all 19 have larger positive effects. The time trend is negative suggesting increases in self-protective behavior. 20

Predictions suggest that returning to baseline levels of activity for retail, transit, and workplaces, will 21 increase R t above 1.0, but not for other activities. Mobility reductions of about 20-40% are needed to 22

achieve an R t below 1.0 (for the upper level 80% credible interval) and even larger reductions to achieve 23 an R t below 0.7. 24

Policy makers need to be cautious with encouraging return to normal mobility behavior, especially 26 returns to workplaces, transit, and retail locations. Activity at parks appears to not increase R t as much. 27 This research also demonstrates the value of using on-line data sources to conduct rapid policy-relevant 28 analysis of emerging issues. 29

Policy measures to reduce the spread of COVID-19 have included "shelter-in-place" orders, shutdowns 35 of sectors of the economy, and requirements for social distancing. These policies, as well as individual 36

protective strategies, have effectively reduced the mobility of people in every country where they have 37 been enacted. In this paper, I examine how mobility reductions are associated with the effective 38 reproduction rate, R t , of COVID-19, and forecast the potential increase in R t should mobility return to its 39 level in January 2020, as well as what level of further mobility reductions are needed to reduce R t to 40 levels that curb spread of the SARS-CoV-2 virus responsible for COVID-19. A key innovation of this work 41

is the use of readily available on-line data sources to address a rapidly emerging crisis. 42

The effective reproduction rate is an indicator of how many people are infected by one individual. Various studies (most published as pre-prints) have examined the effectiveness of specific policies for 57 curbing the spread of COVID-19. An analysis of policies implemented in US states determined that social 58 distancing measures were effective at reducing case-loads, with a lag of up to 15 days (Courtemanche et  59 al., 2020). The same study found no statistically significant reductions associated with school closures 60 and bans on large events; however, "shelter-in-place orders" and bans on restaurant and entertainment 61 centers were effective. Another study evaluated how various policies affected mobility, using Google 62 mobility data for US states (Abouk and Heydari, 2020). Their results suggest that stay-at-home orders 63

were the most effective at reducing mobility while closure of non-essential businesses and restaurants 64 was moderately effective. They found school closures and bans on large events as not affecting mobility; 65

another study found that these two policies also did not affect case-loads (Courtemanche et al., 2020) . It 66 is likely that banning large events is not noticeable in the aggregated Google Mobility data, and school 67 mobility is not one of the mobility factors in the data. Another study found that state shelter-in-place 68 orders were effective at reducing total case-loads after about a three-week lag (Dave et al., 2020 ). An 69 analysis of Google data for US states linked to case reports determined there was a growing incidence 70 over time and that time spent at parks increased the incidence of COVID-19 (Paez, 2020) . 71

These studies suggest that policies aimed at reducing mobility have curbed the number of cases, but 72 they do not estimate mobility effects directly. Reductions in mobility have typically been initiated before 73 lockdown orders were issued. For example, many universities moved to remote learning and limitations 74 on working in the office before lockdowns were issued. Likewise, many firms began limiting employee 75 J o u r n a l P r e -p r o o f travel, for example to business meetings prior to lockdowns. One recent study examined mobility 76 changes in 25 US counties using and found evidence that reductions in mobility reduced growth in cases 77 (Badr et al., 2020) . Other research has demonstrated the effectiveness of lockdowns in reducing R t , but 78

here I focus on the underlying mobility behavior for all 50 states and the District of Columbia, rather 79 than the explicit policy (Arroyo-Marioli et al., 2020). 80

Results show a strong correlation between mobility and R t . Specifically, retail/recreational activity, such 81 as eating in restaurants, office work activities, and public transit usage all are associated with increases 82 in transmission of the virus. Shopping at grocery stores and pharmacies has a smaller association, while 83 affects associated with parks are minor; staying at home reduces transmission. Implications for reducing 84 the spread of the coronavirus are that the reductions in mobility have been effective, but also need to 85 be maintained for longer periods. 86

Mobility data was made publicly available by Google (Google, 2020) and is based upon cell phone 88

tracking data that measures clustering of individuals at six place categories. The places are 89 grocery/pharmacy stores, retail stores/recreation (including restaurants), parks, transit stations, 90

workplaces, and residential locations. The data are anonymized and aggregated by Google and is used to 91 estimate visits and lengths of stays at specific places in Google Maps. The data for each place location 92 and for each country or US state is relative to a median value between Jan 3 -Feb 6, 2020 and changes 93 are relative to the same day of the week and reported as percent changes; data was downloaded on 94

June 26 th , 2020 and was current up to June 23 rd , 2020. 1 An example of the change in mobility is shown in 95 Figure 1 and Figure 2020,Popovich, 2020). As can be seen, time spent at retail, work, and transit locations declined 100

noticeably and even before the lockdowns implemented in each state. Time spent at grocery/pharmacy 101 locations also was lower, suggesting both fewer trips to these locations and less time spent there. There 102 is variability in time spent at parks, primarily due to variation in weather. Time spent at residential 103 locations increased. While these lockdowns clearly affected mobility, it largely coincided with self-104 protective measures that businesses and individuals were already taking. (Badr et al., 2020) also 105 documented reductions in mobility before lockdowns were implemented. Mobility began to gradually 106 increase even before the lockdowns expired. 107 108 interval is provided with the estimates. Given that replicability by doing an updated download is not 127 possible, the full dataset used is available at https://github.com/rbnoland/COVID-data. 128

To evaluate the impact of mobility on R t , fixed effects models that control for state-level effects are 129 estimated. That is, these models control for unmeasured attributes that might affect the dependent 130 variable. A time-trend variable, which starts on the first day that R t is estimated for each state is also 131 included; these start dates vary based on the cases in each state, thus our time trend normalizes for the 132 start of infectious spread in each state. The time trend controls for changes over time and could 133 represent practices such as increased mask-wearing, increased home shopping deliveries, and additional 134 J o u r n a l P r e -p r o o f protective measures taken by firms and individuals. Increasing herd immunity may also be represented 135 by the time trend. Estimates suggest this could be much larger than actual reported cases (Hortaçsu et  136 al., 2020) 137 Standard errors were estimated using a bootstrap with 100 repetitions. This was done as qq-plots 138 suggested some minor deviations from normality in the residuals. However, this made little difference in 139 the standard errors given the high levels of statistical significance in the models and correspondingly low 140 standard errors on the coefficients of interest. 141

The mobility measures provided are all highly correlated, making individual inferences on each 142

impossible if all are included within the same model. Others who have used this data have aggregated it 143

into an index (Arroyo-Marioli et al., 2020). Paez (2020) estimated models with park and workplace 144 mobility only, as these are the least correlated with each other. The models that I estimate include each 145

separately. This allows a comparison of the relative impact of each independently. Models with a 7-day 146 and 14-day lag of each mobility variable are estimated, given that that the onset of symptoms can take 147 almost up to seven days and actual case reports (usually when symptoms are more severe) can take 148

longer. An average incubation period of 11.5 days has been estimated (Lauer et al., 2020) . Estimated 149 models are log-linear, using the log of R t to avoid predictions less than zero. 150

The goal of policy makers is to keep R t below one. A value below one implies that infections are 151 decreasing and aiming for this will result in reductions in total cases and can be effective at stopping an 152 epidemic. 2 The estimates of R t include an 80% credible interval, that is, the actual value has an 80% 153 likelihood of being somewhere within the reported range. Focusing policy on the median value may not 154 be effective, thus additional models using the upper limit of the credible interval are estimated. If one 155 wants greater certainty in the impact of mobility reductions, keeping the upper limit of the credible 156 interval below one is a more risk-averse policy. Predictions are also presented based on the models with 157 a 7-day lag and how this affects the upper level of the credible interval. Finally, I use the models to 158 predict how much mobility needs to be reduced to achieve an upper level credible value of R t = 1 and R t 159 = 0.7, as the latter would be most effective at stopping further spread of the coronavirus. 160

Fixed effects modeling results are presented in Tables 1 -4 for US state-level models. In all cases the 162 coefficients are positive, except for residential locations. That is, increased mobility at locations other 163 than one's residence is associated with increases in R t . This demonstrates the effectiveness of 164 reductions in mobility to reduce the spread of COVID-19. Coefficient values for models with the upper 165 level of the credible interval of R t are slightly larger (Table 2 and Table 4 ). The models have slightly lower 166 coefficient values when the mobility variables are lagged 14 days, but the patterns are similar. 167

Comparing the values of mobility coefficients within each set of models shows that activity spent at 168 parks has the smallest coefficient value, suggesting less viral spread associated with time spent at parks. 169

Other mobility coefficients are generally similar, though grocery/pharmacy coefficients are larger in the 170 models with 7-day lags. Mobility coefficients for residences, while negative, have a larger absolute value, 171

suggesting time spent at home is protective of viral spread. 172

The time trend variable for days since the start of the epidemic in each area is uniformly negative. This 173 variable represents unmeasured effects that change over time. It may be accounting for individual 174 protective actions being taken by people and firms, such as requirements to wear masks or the 175 installation of protective barriers in stores, among other actions. 176 While a return to normal mobility activity will not reduce R t , this leads to the question of how much 210 mobility reduction is needed to achieve an R t = 1. In addition, mobility reductions to achieve R t = 0.7 are 211 also estimated. Using the same model for the upper level credible interval estimates and assuming the 212 time trend up to June 23 rd , 2020, the average across all states and the largest possible mobility 213 reductions needed are shown in Table 6 . Table 7 and Table 8 present the mobility reductions needed by  214 each state to achieve R t = 1 and R t = 0.7, respectively. Large mobility reductions are needed for retail, 215 transit, and work activities for achieving both levels of Rt. Mobility reductions for grocery shopping are 216 also needed to achieve R t = 0.7 and even for parks. The positive values for parks, for R t = 1, mean that 217 additional mobility associated with parks is possible to stay at a value of R t = 1, though to achieve a 218 lower level of R t , mobility would need to be lower than the baseline values (i.e., from Jan 3 to Feb 6, 219 2020). The positive values for residential activity indicate that increases in staying at home are needed 220 to achieve desirable levels of R t . 221 J o u r n a l P r e -p r o o f and pharmacies also seems to not affect R t as much, but additional reductions might be needed to 248

reduce R t below 1. Time spent at home is very effective at reducing R t . A limitation of this work is that 249

we do not know the interactive effects of staying at home versus engaging in other activities; that is, 250 more time spent at home, while protective, means less time spent elsewhere. marking out distances to keep patrons separated may be another factor, as well as resulting in less 258 infectiousness associated with these locations. 259

The predictions estimated suggest that there is still a need for caution in encouraging increased 260 mobility, especially retail/recreational activity, such as eating in restaurants, office work activities, and 261 public transit usage. The models estimated are associative and this means that predictions from these 262 estimates must be considered with care; however, the underlying biology of viral transmission suggests 263 that keeping people distant is effective and mobility reductions are one way to achieve this. Reductions 264 in viral transmission, however, may be temporary, as infections can increase even after substantial 265 reductions in R t , as shown by simulations conducted by Kissler et al. (2020) . 266

Mobility reductions and social distancing are useful policies for reducing peak case-loads, i.e. to "flatten 267 the curve" and avoid overloading health care resources. As of this writing in early January 2021, health 268 care systems are near or at capacity in many parts of the country and R t exceeds 1 in a large majority of 269

states. This is despite mobility levels not returning to baseline levels but also being higher than the 270 reductions seen during the first wave of the pandemic in the Spring of 2020 (see Figure 1 and Figure 2 ). 271

Ultimately, to achieve herd immunity, vaccinations must be administered, which began in December 272

While other studies have demonstrated the relationship between mobility and case-loads, one of the 274 key innovations of this work is the use of readily available data. This allows analysts to quickly conduct 275 analysis of critical issues, virtually in real time to provide guidance to policy makers, demonstrating the 276 value of openly available "big data" to address rapidly emerging issues. 277 278

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R t will exceed one if there is a return to base levels of mobility for retail, transit, and workplaces. Staying at home is effective, while increased activity at parks and groceries/pharmacy has little effect

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