1. Introduction 1 The emergence and global spread of the novel Coronavirus Disease (COVID-19), caused 2 by the SARS-CoV-2 virus, will have a lasting impact on human life. In late 2019, the disease 3 was identified in Wuhan, China and quickly spread across the globe [1] . Nations responded in 4 a variety of ways as cases of the disease increased dramatically within their populations. Some 5 governments responded immediately, severely restricting residents' mobility and pausing most 6 economic activity [2] while others chose to implement less restrictive policies [3] . Across the 7 globe, borders began to close and many national governments chose to close schools and busi-Country or District), and reported in one of six place type categories. Further information on 48 these categories is discussed in Section 3.1. Not only are these data based on one of the most 49 widely used location-based services on the planet, but the data is also passively collected thus 50 reducing the bias of the mobility patterns, as compared to active collection such as surveys or 51 "check-ins" [10] . For the purposes of this research, this data is an ideal representation of ac-52 tivity response to the COVID-19 pandemic and forms the foundation on which we conduct our 53 analysis. 54 As of early May 2020 most governments had responded to the crisis to the degree they are 55 likely to, and many governments had announced plans to lift lockdowns, relax mobility restric- responses? This question helps us understand whether the changes in activity patterns that 69 we see world-wide are actually due to the imposition of government policies, or perhaps 70 due to some other reason, e.g., international media. The differences between countries 71 give insight into differences among governments in their ability to enact the envisioned 72 policies.
RQ2 Which of the six place-based activity categories, as reported by Google, are most affected 74 by policy action? Do these remain consistent between countries? This helps us to iden-75 tify which policies are most effective for influencing human behavior in order to limit the 76 spread of COVID-19, and also which policies are less effective. Since limiting different 77 kinds of activities will lead to different economic outcomes, better understanding this re-78 lationship helps us optimize our responses for the desired outcome.
RQ3 Is there a measurable temporal lag between policy enactment and activity response? If so, 80 does this lag vary between countries? During an exponential growth phase of a disease 81 such as COVID-19 a delay of just a few days can make a large difference in the outcome. 82 Understanding temporal lags between policy enactment and activity response is critical to 83 inform policy-makers who are trying to quickly enact social distancing policies.
RQ4 Does an increase in activity pattern variability within a country (at the subnational level) 85 correlate with a decrease in similarity to government response (RQ1)? This helps us to 86 understand whether a unified, national response is more or less effective than one that is 87 managed by regional and local governments. The remainder of this paper is organized as follows. In Section 2 we discuss existing work 94 on this topic and related topics. An overview of the data used in this analysis is presented in 95 Section 3. Section 4 presents the methodology used in developing the assessment measures and 96 Section 5 show the results of how these measures can be applied to compare and contrast nations. 97 Finally, our findings are discussed in Section 6 and future work and conclusions (Section 7) are 98 presented to the reader. has focused on the regions with early outbreaks. One such study by Kraemer et al. [11] studied 104 the correlation between real-time mobility data from the internet service company Baidu and the 105 spread of the disease in Wuhan, China. The authors found that once the national government 106 established control measures, the correlation decreased substantially. Further work on the trans-107 mission rate of the disease found that travel restrictions enacted by the government delayed the 108 epidemic progression by 3-5 days within China, but significantly slowed the spread elsewhere in 109 the world [12] pointing to the global impacts of the policy actions taken by a single country. Similar work to what we present here has investigated certain economic factors that con-140 tribute to a change in place-based activity patterns (also using Google community mobility pat-141 terns) [30, 31] . These efforts, however, did not look at government policy as a whole or the cor-142 relation of response over time. Other researchers have used this data to predict specific country-143 level responses in the future [32, 33] . To the best of our knowledge, no research has investigated 144 the relationship between government policy action and place-based activity response at the scale 145 we present here, or using the range of methods we propose. The data used in these analyses are publicly available. For reproducibility, links to data 148 sources have been provided as footnotes where appropriate. Data produced from our analysis are 149 available at https://github.com/ptal-io/COVID19-Community-Mobility-Patterns. reports. For this study, we are using activity reports that cover an eight week time period from 160 February 15 to April 11, 2020. The maximum baseline change in the negative direction was 161 100% and 497% in the positive direction (an outlier due to a country-wide festival). An example 162 of these activity patterns are shown in Figure 1 along with the stringency index for the country 163 (introduced in the next section). full methodology for how this stringency index was developed is available at [35] . The dataset is 177 currently being used in a range of preliminary COVID-19 related analysis [36, 37, 38] . ing JavaScript and the D3 framework 9 and is freely available to explore at https://platial. J o u r n a l P r e -p r o o f method for comparing activity patterns to government policy over time due to the fact that it is 210 not invariant to shifts, a feature that is not true for Pearson's correlation. We will use both of 211 these approaches, however, for assessing similarity and report later on the correlation. 
These five activity patterns are expected to decrease with an increase in government policy.
The Residential pattern, on the other hand, is expected to increase as government restrictions 218 increase (see Figure 1 ), so this was not inverted. After these inversions, cosine similarity and Pearson's correlation were calculated between each of the six categories and the stringency index 220 for each country. for each country, C. P G is the place-based activity pattern for G, one of five Google place type 225 category, N = 5 (e.g., Retail). S I C is the stringency index for country C.
We also calculated the average Pearson's correlation coefficient value in a similar manner.
Provided a cosine similarity and Pearson's correlation for each country, we computed Kendall's 228 τ to measure concordance between the two measures. This produced a τ correlation coefficient 229 of 0.602 (p < 0.01), indicating a high level of concordance between these two approaches.
Countries were then ranked based on their average activity pattern to stringency index simi- 
The previous assessment method reported the similarity between the stringency index and 244 the activity patterns overall without explicitly focusing on any one aspect of the curves. In some 245 instances, however, there is a delay effect between the policy enactment and the response. We 246 might see that the slope of the stringency index suddenly increases and three days later that 247 change is mirrored by the activity patterns. In addressing RQ3 we must first test to determine 248 if there is a quantifiable temporal lag between government action and population response. If 249 a lag response exists, we can then identify which countries demonstrate the smallest or largest 250 response lags (LRT ).
The lag response analysis was done using a signal processing approach, calculating the cross- approach is intended to be more robust than looking for the single highest cross-correlation value 266 as it considers skewness in the lag distribution. This is a weighted approach to identifying the 267 peak lag day as a function of all lags above the threshold avoiding an approach that ignores 268 neighboring lag values in favor of a single peak. The results of this subregional similarity analysis were compared to the results of our first 300 cosine similarity assessment approach, the stringency index to country level place-based activity 301 similarities, S MR, using Kendall's τ method. We investigated how our three measures (cosine similarity, lag response, subregional varia-304 tion) align with the spatial relationships of the countries themselves. First, we took a high level 305 approach by calculating the Euclidean distance between each pair of country response vectors.
Each vector is comprised of the six activity categories in each country. Three response similar-307 ity distances were computed for each pair of country vectors. We then calculated the shortest 308 geographic distance between each pair of countries in our dataset. 10 Using the rank correlation 309 approach, we computed the degree to which the geometric distance correlates with each of the 310 response similarity distances. Given the limitations of this approach (non-normal spatial distri-311 bution, and size of countries), we next calculated the similarities in responses of countries based 312 on the continent to which they belong.
Taking a classical (metric) multidimensional scaling approach, 11 we compressed the cosine 314 similarity and lag response distances (again based on vector similarity) into two dimensions in 315 order to visually represent the similarities and differences between the countries in a 2D plot.
While multidimensional scaling is a good visualization tool for displaying similarity between 317 entities such as these, as a dimension reduction technique it does not fully represent all the 318 nuances within the data. Finally, we increased the spatial resolution of our analysis and assessed 319 the similarities in mobility responses between countries that share a border with those that do 320 not. Table 1 .
The results of this analysis identify differences in the relationship of each activity pattern to is not as close to the stringency index with a larger standard deviation across countries than one 405 might expect. Again, some potential reasons for this are discussed in Section 6. Notably, the 406 ranked order similarity for activity categories based on averaged Pearson correlation is the same 407 as that of cosine similarity. choose to go to a grocery store immediately, or a few days after, to stock up on supplies in 422 response to an increase in government COVID-19 related restrictions. Romania also being quite close.
With respect to the subregion variation analysis, the most similar neighboring countries were 495 Italy and France (also highly similar for cosine similarity) followed by the Czechia and Slovakia.
The largest variance was also found in Europe between Italy and Slovenia as well as Switzer-497 land and France. Figure 9 presents a visual representation of these similarities and differences subregions shows no significant concordance with number of confirmed cases, but slight negative 520 correlation (τ=0.165; p<0.1) with number of deaths. As was reported in [35] , there is a strong 521 positive correlation between cases, deaths, and the stringency index. We found, however, that the 522 rank correlation between the average activity pattern and either total confirmed cases (τ=0.610) 523 or deaths (τ=0.569), by country, is lower on average than the correlation between activity patterns 524 and the stringency index (τ=0.631).
In calculating the cosine similarity between the stringency-risk index (cases per capita by the Grocery & pharmacy category, also varied between countries. We noticed weekly patterns in 607 the data indicating that people were still going to work in some countries, even while the transit 608 category remained low and residential was high. This requires further investigation but points 609 towards the variability between country responses, equity issues, and enforcement of policies. 610 We also identified considerable differences in lag time from country to country. Some countries, 611 such as New Zealand, reported virtually no lag between government policy and community re- and lag response values suggesting that countries whose residents responded quickly and with 634 a similar degree of magnitude to the policy actions, were also more likely to respond similarly 635 across subregions.
Exploring the spatial relationships between countries, we found that spatial distribution ex- had little impact on whether or not residents of a country followed their government's advice.
As mentioned previously, the suitability of these indices should be considered when interpreting 674 these results. place-based categories in order to produce a single "within country" variability measure. In 695 many cases we chose to aggregate data either across countries or across place-based activity 696 category. Similarly, there are multiple ways to measure distance between countries. In this work, 697 we choose to measure distance using the great circle distance between closest borders. 