What Matters among Non-pharmaceutical Interventions on COVID-19 in Europe?


 Objectives

The purpose of this study is to describe the situation of the COVID-19 in European countries and identify important factors related to prevention and control.
Methods

We obtained data from World Health Statistics 2020 and the Institute for Health Metrics and Evaluation (IHME). We caculated the Rt values of 51countries in Europe under different prevention and control measures. We used lasso regression to screen factors associated with morbidity and mortality. For variables selected, we used quantile regression to analyze the relevant influencing factors in countries with different levels of morbidity or mortality.
Results

The government has a great influence on the change of Rt value through prevention and control measures. The most important factor for personal and group prevention and control is the mobility index, testing, the closure of educational facilities, restrictions on large-scale gatherings, and commercial restrictions. The number of ICU beds and doctors in medical resources are also key factors. Basic sanitation facilities, such as the proportion of safe drinking water, also have an impact on the COVID-19 epidemic.
Conclusions

This study describes the current status of COVID-19 in European countries. We found key factors in individual prevention and control measures and group prevention and control measures.

closure of educational facilities, prohibition of public gatherings, all commercial activities and non-essential commercial activities. The effect of prevention and control may also be related to medical resources, such as doctors, nurses, pharmacists, ventilators, ordinary beds, and ICU beds. The country's economic situation and ability to respond to public health incidents. For example, GDP and GHS may be related to the effectiveness of prevention and control.
The World Health Organization recommends a variety of measures: rapid diagnosis and immediate isolation of cases, strict tracking and preventive self-isolation. Switzerland regards testing as the main method to control COVID-19 3 . Widespread testing for COVID-19 will draw a clear picture of the dynamic of the COVID-19 epidemic. Without clear numbers, it will be very di cult to evaluate whether control measures were effective. A meta anlysis showed that medical masks and N95 masks can protect against viral respiratory infection including coronavirus 4 . Community-wide mask wearing can contribute to the control of COVID-19 by preventing contact with large amounts of saliva and respiratory droplets from asymptomatic COVID-19 patients 5 . Hand hygiene is the most important factors of control activities and infection prevention because it reduces the quantity of microorganisms on your hands and minimizes the possibility of transmission to other people 6 . The use of antiseptic hand soaps offered a greater reduction in the number of microorganisms compared with regular soaps 7 . However, toxicity and stability of surface disinfectants, are the issues that should be further investigated 8 . Governments have advocated by implementing physical distancing and self-isolation and reducing outdoor activities in many counrties. The ndings of a systematic review and meta-analysis support that physical distancing of 1 m, face masks, and eye protection to prevent person-to-person transmission of COVID-19, Which ones are relevant to the best evidence currently available and can be used for interim guidance. The randomized conrtol trials are needed to better inform the evidence for these interventions 9 .
The rst country in Europe where the COVID-19 outbreak was Italy. On 9 March 2020, the Italian government implemented a comprehensive "blockade" policy, mainly consisting of travel restrictions, mandatory staying at home (except for health problems, emergencies or regulated shopping for necessities) and temporary closure of nonessential businesses and shops, which lasted until 3 May 2020. In the following months, many European countries also adopted similar measures 10 . In March 2020, 47 countries did not allow commercial ights to land. This can stop the development of this virus, but we should work together 11 .What's more, It is necessary to develop an international framework that outlines the method, time and scale of travel restrictions according to the stage of the epidemic 12 . A cross-sectional study suggests that issuing a stay-at-home ban may help limit the spread of COVID-19 cases in Iowa 13 . On March 12, Norway issued stricter measures and instituted quarantine for those who entered the country. The same day, the government closed all schools and kindergartens, psychologists,physiotherapists, hairdressers, psychologists training centers and swimming pools, forbided cultural and sporting events. Sweden chose a different strategy: kindergartens, elementary schools, other businesses and training facilities continue to open, and children's sports continue 14 . Mass gatherings are related to the high transmission rate of SARS-CoV-2, and many sporting events have been restricted or canceled to limit disease spread 15 . Some non-essential business such as vape shop were closed 16 .
The disease incidence, daily cumulative index, mortality of COVID-19 were relatived to country healthcare resources and economic status 17 . In Italy, 16% of hospitalized COVID-19 patients require intensive care. Compared with Germany, the medical resources in northern Italy are overwhelmed by the increase in patients. In contrast, Germany has a wider distribution of cases and can make better use of resources. For every 100,000 population, Germany has more intensive care beds than Italy. The high mortality rate in Italy may re ect the relationship between the availability of medical resources and outcomes 18 . In addition, the prevention and control effect of COVID-19 may be related to indications such as GDP(Gross Domestic Product)and GHS(Global Health Security Index) 19 .

Research objective and data sources
We obtained data from World Health Statistics 2020 and the Institute for Health Metrics and Evaluation (IHME). The IHME is an independent population health research center at University of Washington Medicine, part of the University of Washington, that provides rigorous and comparable measurement of the world's most important health problems and evaluates the strategies used to address them. We selected 51 countries in Europe as our research objective. There are 53 countries in Europe according to WHO regional groupings. The data of Monaco and Turkmenistan is incomplete, so we discarded these two countries. Where does IHME obtain its data? These forecasts include data from local and national governments, hospital networks and associations, the World Health Organization, third-party aggregators, and a range of other sources.
For testing data, IHME rely primarily on data reported by Our World in Data. However, for Cyprus, Italy and Spain, they used government data. IHME obtain hospital resource data from sources such as government websites, hospital associations, the Organisation for Economic Co-operation and Development, WHO, and published studies. For population density, They used gridded population count estimates for 2020 at the 1 x 1 kilometer (km) level from WorldPop. For mobility index data, IHME used anonymized, aggregated data from Google, Facebook, and Apple. Their data on mask use come from Premise, Facebook Global Symptom Survey (research based on survey results from the University of Maryland Social Data Science Center), Kaiser Family Foundation (KFF), and YouGov COVID-19 Behaviour Tracker survey.

Statistical Analysis Method
We described the changes in the Rt values of 51 European countries under different prevention and control measures. We also analyzed and evaluated the prevention and control effects of COVID-19 in European countries. We used Lasso regression to screen factors related to morbidity and mortality. For the selected variables, we used quantile regression to analyze relevant in uencing factors in countries with different morbidity or mortality.

Changes of Rt under different prevention and control measures
There are roughly four methods for estimating Rt, exponential growth method, maximum likelihood method, sequential Bayes method, and time-dependent basic regeneration number method. In this study, we used the time-dependent basic reproduction number method, and we mainly focused on the time-dependent reproduction number (Rt). Rt is the average number of secondary cases of a single infected person during the t day of infection. Rt is usually used to describe the transmission characteristics of pathogens during a disease epidemic, and it can also evaluate the effectiveness of interventions. When Rt is greater than 1, it indicates that the number of infections is increasing rapidly; when Rt is less than 1 and close to 0, it indicates that the epidemic has been effectively controlled 20 .

Lasso Regression
Two methods of variable selection in linear regression model mainly include subset selection method and coe cient compression method. The traditional linear regression method belongs to subset selection method and the main method to screen variables is the least square(OLS) method. However, this method has some defects: variable selection is separated from model parameter estimation, so the model error increases; Small changes of variables have great in uence on variable selection. Variable selection is not suitable for high dimensional data 21,22 . With the booming eld of machine learning, there has been growing number of statistical tools compensate for the limitations of traditional methods. The least absolute shrinkage and selection operator regression (lasso regression) is the representative regularization method can effectively optimize OLS estimation and treatment Over tting problem 23 . By introducing penalty term into model estimation, Lasso method can obtain higher prediction accuracy and model generalization ability. It also can effectively deal with over tting and multicollinearity problems [24][25][26] . The speci c formula can be expressed as: The rst part represents the standard OLS loss function, the second part represents the penalty function. It represents the tuning parameter for controlling the degree of regression coe cient compression, when λ is ≥ 0. the greater the value, the stronger the penalty will be. When λ=0, The loss function does not penalize the model. Lasso regression shrinks some coe cients and sets others to 0 and tries to retain the good features of both subset selection and ridge regression 27

Quantile Regression
Quantile regression (QR) is a method of estimating the linear relationship between the different quantiles of the dependent variable and the independent variable. Both QR and original linear regression (OLS) can be seen as solutions to speci c minimization problems. The estimation of OLS regression is based on the smallest residual square, and the estimation of QR is based on the smallest weighted absolute value residual. The minimum weighted absolute deviation of quantile regression is as follows: The essence of quantile regression is to calculate the regression coe cients of different quantile values of the dependent variable. It can comprehensively display all data information to a certain extent, but it focuses more on the overall heterogeneity analysis of features distributed in different locations. It can not only measure the in uence of regression variables in the center of the distribution, but also the in uence on the upper and lower tails of the distribution. Therefore, it has unique advantages over traditional linear regression models and can obtain comprehensive analysis results. Especially for the condition of uneven distribution, quantile regression is more comprehensive and accurate than traditional linear regression coe cient estimation 31 .

Results
Our results are divided into 3 parts. First, we calculated the changes in Rt under different prevention and control measures. Secondly, lasso regression screened 17 variables that were relative to cumulative mortality and cumulative morbidity, and nally lasso regression screened out meaningful variables for quantile regression. Subsequently, the Rt value dropped to around 1. On October 16, there was a small peak of 2.51. The graphs of Rt changes in other countries can be seen in the supplement materials.

Result of Lasso Regression
In this study, the relationship between 2 dependent variables and 17 independent variables was explored, including cumulative morbidity (Y1) and cumulative mortality (

Results of the Quantile Regression
The results of quantile regression are different from the results of lasso regression, and quantile regression provides more comprehensive information. The speci c content is presented in Table 1. The changes of coe cients and con dence intervals in quantile regression are shown in Fig. 3. The overall result is that the mobility index, the ratio of safe drinking water, and the closure of non-essential businesses are related to the cumulative incidence. Educational facilities closed, any gathering restrictions, Non-essential businesses close are related to cumulative mortality. In low-and medium-incidence countries, the total number of tests is related to the cumulative incidence. In high-incidence countries, closed educational facilities and any gathering restrictions are related to cumulative mortality.

Discussion
Our study found that the population prevention and control measures implemented by the government had an impact on the change of Rt value. In most countries, the Rt value has a clear upward trend in October. The most important factor in personal prevention and control is the mobility index. Group prevention and control on the total testing, closure of educational facilities, restrictions on large-scale gatherings, commercial restrictions and other government interventions are very important for prevention and control. The number of ICU beds and the average number of doctors in medical resources are also key elements. Basic sanitation, such as the proportion of safe drinking water, also has a certain impact on the COVID-19 epidemic.
The rate of masks using in individual prevention has not been found to be related to cumulative mortality or morbidity. It does not mean that the use of masks has no effect on prevention and control. Research on the effectiveness of masks for prevention and control has been con rmed 4 . The lasso regression nds variables with a very large degree of correlation, so the mobility index generated by personal behavior in the movement of personal behavior in prevention and control may be more important than wearing a mask. Secondly, we think the possible reason is that the data on the rate using of masks comes from social surveys and there may be large errors.
Some studies have reached conclusions consistent with ours. The results of the dynamic SEIR model show that the lockdown control measures implemented by China on January 23, 2020 are essential to ultimately reduce the scale of the COVID-19 epidemic 32 . A study found that the effectiveness of different interventions varies. They estimated that early detection and isolation of cases prevented more infections than restrictions on travel and reduced contact. Non-drug interventions should be combined to achieve rapid results. Our research also found that there is a certain relationship between cumulative mortality and testing 33 .Some scholars even proposed that the best strategy is to use both robot recognition and migration restriction strategies. In China, robots are assigned multiple tasks to minimize the spread of COVID-19, such as using them to clean and prepare food in epidemic areas that are harmful to humans. European countries can also take this approach to reduce exposure to infection and provide help for the prevention and control of diseases 34 . Once the initial pandemic is under control, we must turn our attention to how to improve the adverse effects of the lockdown 35 .
Studies have also shown that medical resources are related to the mortality rate of COVID-19, which is close to our research conclusions. We have found that the number of doctors per capita and the number of hospital beds per capita are related to the incidence or death of COVID-19 36 . The experience in Wuhan suggests that if the medical resources become scarce, the government should establish temporary hospitals and Medical staff will be deployed from areas where the epidemic is relatively mild to ease the pressure in severely affected areas.
Effective quarantine via quick detection prevent a larger outbreak 37,38 . It is necessary to eatablish medically necessary, time-sensitive procedures scoring system during the COVID-19 Pandemic 39 . Within days or weeks, the health system is reorganized. We must optimize health resources. Fight for disease in a joint medical team composed of doctors, nurses, pharmacists, and respiratory therapists 40 .
The ratio of safe drinking water in basic health resources has a certain relationship with the cumulative morbidity and mortality of COVID-19, which may be related to the fact that hand washing can reduce the number of hand viruses and achieve a certain prevention and control effect. Basic cleaning services are a basic prerequisite for compliance with the principles of infection prevention and control, which are necessary to protect patients, health workers and susceptible people 41 .
Some indicators, such as nurses per capita, pharmacists per capita, GDP and GHS, are not included in the regression model, which may be due to the relatively low correlation degree. After the Ebola outbreak in 2014, the Global Health Security Index (GHSI) was developed to measure the ability of countries to respond to infectious disease outbreaks. Six core elements were evaluated: prevention, detection and reporting, response, health system, compliance with norms and the risk of infectious disease outbreaks. The score higher of GHSI, the better the preparation.
Studies have shown that GHSI and JEE (Joint External Evaluation) have low predictive value for the death outcome of COVID-19, and we have reached the same conclusion 42,43 . For example, UK, which ranks second in GHSI score, also bears a huge burden of disease 44 . However, some studies have shown that GHSI has a predictive effect on the burden of COVID-19, but in the opposite direction 45 .
Our research has some advantages. First, this study describes the prevalence and control of COVID-19 in European countries and the workload is relatively large. Secondly, this study included many independent variables to analyze their relationship with dependent variables. The independent variables mainly include individual prevention and control, group prevention and control, medical resources, basic health facilities, and comprehensive indicators. Thirdly, this paper uses lasso regression to screen variables with a smaller error than traditional regression and the results are more accurate. Quantile regression is further used to quantify the speci c situation of each divided point, which provides more information than traditional regression. Of course, our article also has some shortcomings. For example, a small number of proven effective prevention and control measures have not entered our regression model, which may be related to the accuracy of the data and the impact of variables.

Conclusions
This study comprehensively describes the current status of COVID-19 prevention and control in European countries. We found key factors in individual prevention and control measures and group prevention and control measures, which can provide a policy basis for the prevention and control of epidemics in European countries.

Declarations
Ethics approval and consent to participate Not applicable.

Consent for publication
Not applicable.

Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Authors' contributions YL acquired the data, performed the analysis of data, and wrote the manuscript. QY and HW acquired the data and contributed to the analysis of data. FS , FW and YZ contributed to the coding of the statistical analysis. CY evaluated the whole work.