The impact of mask-wearing in mitigating the spread of COVID-19 during the early phases of the pandemic

Masks have been widely recommended as a precaution against COVID-19 transmission. Several studies have shown the efficacy of masks at reducing droplet dispersion in lab settings. However, during the early phases of the pandemic, the usage of masks varied widely across countries. Using individual response data from the Imperial College London—YouGov personal measures survey, this study investigates the effect of mask use within a country on the spread of COVID-19. The survey shows that mask-wearing exhibits substantial variations across countries and over time during the pandemic’s early phase. We use a reduced form econometric model to relate population-wide variation in mask-wearing to the growth rate of confirmed COVID-19 cases. The results indicate that mask-wearing plays an important role in mitigating the spread of COVID-19. Widespread mask-wearing associates with an expected 7% (95% CI: 3.94%—9.99%) decline in the growth rate of daily active cases of COVID-19 in the country. This daily decline equates to an expected 88.5% drop in daily active cases over 30 days compared to zero percent mask-wearing, all else held equal. The decline in daily growth rate due to the combined effect of mask-wearing, reduced outdoor mobility, and non-pharmaceutical interventions averages 28.1% (95% CI: 24.2%-32%).


Introduction
In response to the COVID-19 pandemic, multiple countries curbed the spread of the disease by enforcing strict policy measures such as lockdowns and shelter-in-place orders [1]. The non-pharmaceutical interventions (NPIs) included closures of schools, restaurants, bars, retail outlets, and other non-essential businesses, as well as shelter-in-place policies and the prohibition of large gatherings (e.g., limited to 10 people) [2]. These institutional measures aimed to reduce the exposure of susceptible individuals to symptomatic and asymptomatic infected individuals by decreasing outdoor mobility (e.g., going out to movies, concerts, and

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How mask-wearing mitigated  to different measures of mobility. We note that neither Google nor Apple provide absolute mobility measures, but rather present relative changes to benchmarks they use internally. Finally, drops in mobility could be driven by both individual actions (e.g., cautious behavior) and institutional actions due to NPIs enacted by governments. To control for mobility declines due to institutional actions, we also include country-specific interventions enacted both nationally and provincially. Non-pharmaceutical interventions. Governments across the 24 countries enforced different policies to control the spread of COVID-19. Prior research has shown that these policies played a significant role in reducing the human to human physical contact and led to a slowdown in the spread of the disease. However, these policies were implemented at different levels, some nationally, some provincially. We use data from the COVID-19 Government Response Event Dataset [1] to control for government policies in estimating the effect of masks. Fig J in S1 Text lists the types and counts of national and provincial government policies implemented across the 24 countries we consider in this study. The dataset contains 5,816 entries on policies at the national and provincial levels. Finally, the inclusion of these interventions helps control for some of the observed drops in mobility that are not necessarily associated with individual actions but with the presence of institutional policies. S1 Text includes the detailed information about the interventions.

Covariates
Because the data span multiple countries and weeks, we include time and country fixed effects in the model. The model controls for country-level heterogeneity using fixed-effects, where the variable for a country assumes a value of one if the data considered are specific to that country and zero otherwise. This variable allows for control of country-level characteristics that are not in the model and helps reduce the errors due to omitted variables in our analysis. In addition to country-level differences, we also control for time-based differences (e.g., people are more aware and cautious over time) by incorporating time-fixed effects, where the variable Week t takes a value of one if the data are from week 't' (where t = 1 represents the first week for a given country in the data). In addition, we control for each country's testing capability ( Fig  3A) by accounting for the country's total number of daily tests. Finally, we also control for people's actions to educate themselves by including the Google Trends ( Fig 3B) data for the search term 'coronavirus'.

Outcome variable
Data for the number of active daily cases in each country were obtained from the Johns Hopkins University School of Public Health [21]. We use a seven-day moving average of cumulative confirmed cases and cumulative recovered cases to compute daily active cases and daily growth rates. The daily growth rate is the ratio of active infections today to active infections the day before. The dataset aggregates this information across multiple national, state, and local health departments within each country. The daily growth rate is then related to the independent variables described earlier through a reduced-form econometric model. We describe the derivation in detail (Section S1Text). We illustrate the daily cases and growth rate for one country, Italy, in

Analysis
We use a reduced form econometrics model to relate the growth rate of daily active infections to the independent variables described earlier. Similar models have been used by [3] to determine the effect of anti-contagion policies on the spread of COVID-19. In brief, the model  assumes that the daily growth rate (ratio of active infections today to active infections the day before) is affected by institutional measures such as NPIs and individual measures such as outdoor mobility and mask-wearing. The covariates listed above help control for other factors that could affect growth over time. The method also has roots in compartmental epidemiology models-SIR (Susceptible, Infectious, Recovered). Because the epidemiological parameters for new diseases such as COVID-19 might not be well understood, reduced form techniques allow for the estimation of the impact of governmental and personal measures to help contain the spread of the virus. To filter out the high variation in growth rates when the number of cases is very low at the beginning of the pandemic, our model for each country initializes when a country reaches 20% of peak new cases, as observed by July 8, 2020. For robustness, we also test other starting times in the Supplements and find results in line with the ones presented here. SIR growth rate model. Eqs 1-4 describe the SIR model where S j,t , I j,t , and R j,t show the active susceptible, infectious, and recovered population at time t in country j. β j is the rate of transmission and γ j is the rate of recovery in country j. Since we do not consider reinfection and deaths, γ j can be considered as the rate of removal from infectious population. N j is the total population of the country j. Eq 1 shows how infections spread from the infectious individuals to susceptible individuals. Eq 2 shows how the infectious population changes over time as some susceptible individuals contract the disease while some already infectious individuals recover from the disease and test negative. Eq 3 shows how the number of recovered individuals increase over time as individuals recover after testing negative for the virus. Eq 4 is a feasibility constraint which ensures that the total population is accounted for in the model. Addition of Eqs 1-3 yields Eq 4.
Since we model only the growth rate in the total confirmed cases, we consider Eq 2 in our analysis. Assuming S j,t �N j (at the early stages of the pandemic), we can solve Eq 2 by integration. Details of analysis are provided in the S1 Text. If we consider daily growth rate (t 2 −t 1 = 1), the growth rate model can be simplified as shown in Eq 5, where g j is the growth rate and it is given by β j −γ j .
Wearing face masks, reducing social mobility, and the implementing of NPIs can alter the growth rate by changing g j . Eq 6 represents the growth rate model (P is the set of policies; M is the set of indicators of social mobility, W is the set of weeks for the duration of our analysis, and J is the set of countries in our analysis). mobility j,t,m is the m th indicator for social mobility, week j,t,w = 1 if day t in country j is in week w after the initialization point for country j. The starting point of analysis for each country could vary as explained earlier. � t is the gaussian error term in Eq 6. The rest of variables are as described earlier (and with more detail in the S1 Text).
The econometrics approach of using the growth rate to estimate the effects of masks, social mobility, and NPIs has several advantages. The model can estimate the effect of the exogenous independent variables on the dependent outcome variable (growth rate). Since the left-hand side of Eq 5 can be empirically calculated, it does not explicitly require the knowledge of the relationship between exogenous variables and I j,t . Thus, the model does not need to know the link between masks, NPIs, and social mobility on daily active cases (or cumulative confirmed cases) but can still estimate their effect on the growth rate of infectious cases. Using the growth rate, I j,t can be estimated by integrating it from time 0 (or using previous integration up to the day t−1). Thus, this model is forward-looking. The S1 Text also provide further details about the methodological approach and model formulation used in this paper.
We provide some brief notes on the operationalization of the independent variables and the model initialization below: 1. The growth rate model is able to handle underreporting in COVID-19. In the COVID- 19 pandemic, data for an individual is recorded when only they are tested. Total confirmed cases (deaths and recovered cases) in publicly available datasets only provide information on the individuals who got themselves tested. Due to various reasons, e.g., lack of testing, lack of motivation to get tested, or lack of visible symptoms in asymptomatic cases, it is being estimated that there is a massive underreporting in total confirmed positive cases. However, the growth rate model is agnostic to underreporting as it models the first difference in the log of confirmed cases. If the underreporting is a constant proportion of the reported cases, we can multiply I j,t and I j,t−1 with a constant factor, and it would not affect our estimation of growth rate (Eq 5).
2. Responses to the survey about mask-wearing are subject to biases. For example, individuals might overestimate the efficacy of their mask or their wearing pattern. To alleviate some of these concerns, we compute the natural log of the mask-wearing variable to discount its impact on the growth rate of daily active cases. This transformation yields a curve that grows at a slower rate as the values of mask-wearing increase, thereby diminishing the impact of higher levels of mask-wearing. We also test for other functional forms (squareroot and linear) and present those results (Table G in S1 Text).
3. Due to the high correlation across the different mobility data categories obtained from Google, we only include the categories of Mobility: Parks and Mobility: Transit Stations in the model. Because we are interested in determining the impact of mobility in general, these two mobility variables suffice in capturing the individual's movement patterns during this time. In S1 Text, we present results including other mobility types and also run the model with Apple Mobility data in place of Google Mobility Reports.
4. The CoronaNet dataset from [1] collected information on all the government policies introduced by different countries across the world. They categorized the policies into 19 different policy types. We use their categorization in the model. From February 21, 2020 to July 8, 2020, we check if a policy p was implemented in a country j on the day t. If the policy was implemented, we assign a value of 1 to s j,t,p , where s represents the level of policy coverage. If the policy was introduced at a provincial level, we normalize s j,t,p by the population of the state. Because several policies were introduced simultaneously or close together, they suffered from collinearity issues. To minimize multicollinearity issues, we choose only a specific set of policies to include in the analysis; S1 Text discusses this selection mechanism.
5. Due to the uncertainty of the lag in COVID-19 incidences and the difficulties in detection during the early days of the disease [22,23], similar to prior research, we tested the focal model across multiple lag periods (shift) from zero to 14 days and for different initialization thresholds (th) for each country (0% to 20% of a country's peak daily cases by July 08, 2020). We chose the best shift and th values using a k-fold cross-validation process (k = 5). The chosen model had the highest maximum likelihood estimate of the data and the lowest prediction error. We discuss this procedure (Section S1 Text). The results presented in the next section correspond to a model with a shift of nine days and a th of 20% of peak new cases by July 08, 2020. Finally, we train the model on 1,422 daily case observations across 24 countries. These observations span from the day each country's daily cases reached 20% of its peak to July 08, 2020. We restrict our analysis to the first 60 days after model initialization based on th. However, we test the robustness of the findings for other lengths of data. This allows for greater variation in mask usage within the data.
In the next section, we describe our results and their policy implications.

Results
The results indicate that individual measures such as mask-wearing and outdoor mobility combined with institutional measures (NPIs) play a role in mitigating the spread of COVID-19. Fig 5 shows the estimates from the focal reduced-form model for these measures and their corresponding confidence intervals. The full table of results, along with results for all robustness checks, are provided in S1 Text. We first list the results of the key measures we consider and then discuss their implications.

Mask-wearing
The model finds that reported mask wearing of 100% associates with an average 7% (95% CI: 3.94%-9.99%) drop in the daily growth rate of COVID-19 cases. While this daily effect appears small, 100% reported mask-wearing leads to approximately 88.5% (95% CI: 68.7%-89.2%) decline in active cases over 30 days compared to the situation where 0% of the people report wearing masks (all else remaining the same across the two scenarios). Modifying the functional form of the mask variable did not appreciably change the association. For example, in the linear model, masks are associated with an average 8.69% (95% CI: 5.63%-11.66%) drop in daily growth rate, and for the square root model, the expected daily drop in growth rate was 7.89% (95% CI: 4.81%-10.87%). The stability of the results indicates that mask-wearing plays a significant role in mitigating the spread of the disease. Fig 5 also illustrates that widespread mask-wearing, as an intervention by itself, has the most significant association (by magnitude) with the growth rate of active COVID-19 cases. Fig 6 plots the ratio of active cases under different proportions of respondents who claim to wear masks against no mask-wearing and for various periods.

Mobility and NPIs
As expected, the model finds that a rise in mobility links with a rise in the number of cases. Specifically, the selected mobility variables associate with a combined 8.1% (95% CI: 5.6% -10.6%) drop in daily case numbers. Similarly, we find that the implementation of NPIs is also associated with a drop in daily growth rates across countries. After accounting for mobility declines, the NPI measures 'Quarantine', 'External Border Restrictions', and 'Closure and Regulation of Schools' link with the highest declines in the growth rate of daily active cases. Overall, all NPIs included in the model led to a decrease in the growth rate of COVID-19. This finding confirms multiple studies that investigated the effects of NPIs on limiting the spread of COVID-19 [10,13,23,24]. Overall, we find that if the NPIs were enacted uniformly across the whole country, then the combined association of the NPIs with the decline of growth in daily cases of COVID-19 would average 13% (95% CI: 9.2% -16.2%). We determine the combined effect using the Krinsky-Robb method, a Monte Carlo simulation used to draw samples from a multivariate normal distribution. S1 Text provides more details on this method.

Controlling for endogeneity using control functions
Due to nearly concurrent enactments and blanket coverage of policies and precautionary behaviors within countries, the individual (e.g., masks, limiting mobility) and institutional (NPIs) measures correlate in time. This precludes the causal identification of each measure's effect on disease mitigation. In other words, because mask-wearing, mobility reductions, and NPIs occur at similar times, their effects are intertwined and difficult to determine separately. For some variables, such as mobility and NPIs, we lack the necessary data to fully control for these issues. In the case of mask-wearing, even though we cannot eliminate all the possible endogeneity issues, we attempt to alleviate some of the concerns of confounding variables by employing control functions [25]. As noted in [26], control functions make the intervention exogenous in a regression equation. To create a control function, we use mortality data for prior outbreaks of SARS, H1N1, and MERS in each country as instrumental variables to predict the proportion of mask-wearing in each country (see S1 Text for more details). We posit that exposure to prior pandemics would have resulted in a more aware populace that could be amenable to precautionary behaviors such as mask-wearing. Next, we compute the control function by determining the predicted mask-wearing residuals (computed via determining "Predicted Mask-Wearing minus Reported Mask-Wearing"), allowing for better identification of the effect of reported mask-wearing on COVID-19 case numbers. Using this procedure, we find that if 100% of the population claimed to wear masks, then mask-wearing relates to an average 4.95% (95% CI: 2.26%-7.53%) drop in the daily growth rate of COVID-19, when compared to zero percent reported mask-wearing. Over 30 days, this translates to a 70.4% (95% CI: 62.3%-72.7%) drop in new COVID-19 cases. While we are careful to note that this estimate could still be affected by confounding variables, this result lends stronger support to the magnitude of the disease mitigation that mask-wearing in the general population provides. In summary, widespread mask-wearing leads to a significant decline in the spread of COVID-19.

Robustness checks
To help determine the accuracy and stability of the results, we run several robustness checks (see S1 Text for details): 1. We vary the lag period (shift) from 0 to 14 days. The results show that the estimates of the individual and institutional measures are relatively stable. 2. We also vary the length of time we consider in the analysis. The model considered 60 days of data for each country. We vary this to estimate the model on 35,45,55,65,75, and 85 days of data and find that the results remain stable to these variations.
3. We replace Google mobility data with Apple mobility data. The model estimates remain robust to this change.
4. We vary the functional form of how mask-wearing relates to the spread of COVID-19. The results are not statistically different in these cases.

5.
We also test the robustness of the analysis by modifying the data using exponential smoothing. Specifically, for any day t, the focal model in Eq (1) ignores the value of the independent variables from days t-shift+1 to t (discussed in Fig A in S1 Text). In the model we use for the robustness check, we do not ignore values between t-shift and t and use exponential smoothing to average the intervening data. Finally, we also modify the interpolation method of mask-wearing data from linear (current) to quadratic. We find that the results are stable with all these modifications.
The S1 Text detail all the robustness checks and simulations as well as their results.

Discussion
Over the past few months, several studies have investigated the efficacy of masks at minimizing droplet dispersion [27,28] and the potential consequences of their use [14,29] in the general population. Although a randomized control trial on the efficacy of face mask usage appears to indicate inconclusive results in the general population [15][16][17] provide evidence for the benefits of face mask usage through a systematic review of the multiple observational studies and the evidence thus far. While the type of face mask, as well as the timing and length of use, can affect its efficacy, its use as a precautionary principle has been strongly advised [30]. Despite the abundant scholarly and some anecdotal evidence [31], face mask use in some countries like Sweden and the United States remains controversial [32][33][34]. Additionally, as observed in the data, even in countries where masks do not face similar headwinds and as support for mask usage gathers further evidence, face mask use is not as commonplace (e.g., Denmark, Norway, Sweden, Finland), even as a precautionary principle. This study links the growth rate in active cases of COVID-19 in a country to a population's reported wearing of face masks in public places over time. The model also includes other measures that could simultaneously impact the spread of the disease as face mask usage changes over time. After accounting for these measures and controlling for other covariates, the results indicate that reported face mask use is associated with a decline in the growth of COVID-19. More precisely, if 100% of the population claimed to wear masks, then mask-wearing is associated with an average 7% decline in the growth of daily active cases of COVID-19. This association persists across multiple robustness checks and model formulations. A decline of 7% corresponds to an 88.5% drop in the number of active cases 30 days later. Together with the other measures (mobility changes, NPIs), the combined association of individual and institutional measures on the decline in the growth rate of daily active cases of COVID-19 is 28.1% (95% CI: 24.2%-32%).

Limitations
Countries enacted multiple NPIs simultaneously. This precludes us from identifying the effectiveness of NPIs separately. Second, the mobility data provided by Google and Apple are only indicative of the relative changes from a benchmark, so their association with disease spread should be interpreted with precaution. Third, we rely on the accuracy of data collected by third parties like YouGov. Inconsistencies in testing, reporting, and recording the data could lead to errors in the results obtained. Additionally, mask types and mask-wearing patterns could vary across countries, individuals, and over time. Finally, individuals might wear masks incorrectly, might wear less effective masks, or might misreport their mask-wearing behavior. For example, using data across the US and Canada, [35] show that mask-wearing differs based on negative attitudes toward SARSCoV2 vaccination, beliefs that the threat of COVID-19 has been exaggerated, disregard for social distancing, and political conservatism. Cultural collectivism has also been shown to have a significant effect on mask usage. For example, [36] show that collective interdependence and state-level differences in collectivism were good predictors of mask usage. Similarly, using data from all US states, 27 countries and from [37] also find that culturally collectivistic regions are more likely to wear masks. These differences and limitations affect the validity of all COVID-19 population-based mask-efficacy studies.

Conclusions
The population-wide usage of face masks as a preventative measure against the transmission of COVID-19 varies widely across countries. Using data from 24 countries, this study finds that face mask usage associates with a decline in the growth rate of daily active cases of COVID-19. Over a 30-day period, mask-wearing associates with an 88.5% decline in the number of daily active cases. This result re-affirms the prominent importance of masks in combating the spread of COVID-19.