key: cord-0937852-zvd4z25e
authors: Assoumou-Ella, Giscard
title: Total containment of the population and number of confirmed cases of covid-19 in England, Belgium, France and Italy
date: 2020-12-10
journal: New Microbes New Infect
DOI: 10.1016/j.nmni.2020.100834
sha: 6a40a4476585d2132de0e8de18a3ca2080552058
doc_id: 937852
cord_uid: zvd4z25e

We analyze the impact of total population containment on the evolution of the growth rate of confirmed cases of covid-19 by controlling the results by the situation observed in a country that has not applied this measure. We conduct the study in four European countries, namely England, Belgium, France and Italy, taking Sweden as a control country that did not confine its population. To do so, we use the Interrupted Time Series Method (ISTA). Comparisons of the post-intervention linear trends of covid-19 confirmed cases from England, Belgium and France with that of Sweden show no statistically significant difference. Comparison of the post-intervention linear trends of covid-19 confirmed cases from Italy with that from Sweden shows a positive and statistically significant difference. It reflects a dynamic in the growth rate of confirmed cases in Italy higher than that observed in Sweden despite the total containment of the population. The results obtained therefore lead to the conclusion that the measure of total population containment is ineffective in the countries of the sample. They suggest that the evolution of confirmed cases of covid-19 could be the result of a combination of other factors, and not specifically of total population containment.

, which was officially discovered in Wuhan in December 2019, has impacted not only infected but also uninfected people in most countries. Indeed, there are to date from 27/11/2020, 60973636 confirmed cases, 39069813 cures and 1432047 deaths worldwide.

In order to contain the progression of the virus, apart from medical care, social restriction measures have been taken by governments. Among these, total containment of the population has been presented as a flagship measure that can achieve this goal. In Western Europe, it has been applied in many countries, particularly in England, Belgium, France and Italy. Indeed, on March 14, 2020, England announced the total containment of its population. On March 17 of the same year, France and Belgium do the same. Italy had already announced the total containment of its population on March 10, 2020.

The application of this restrictive measure is based on the assumption that social distancing in times of epidemics slows the spread of the virus by limiting the number of contacts between infected and uninfected people. This assumption is based on the pioneering work of Kermack and McKendrick (1927) , and recently of Vrug et al (2020) who developed models showing the effectiveness of social distancing measures and isolation in slowing the spread of epidemics.

With the fear of a new rebound of the epidemic in many countries at present, total population containment is once again evoked by some governments. However, the possibility of a return to total containment in several countries and the application of other social restriction measures are causing some concern, as are currently seen in the demonstrations against the restriction of freedoms in many western metropolises.

However, scientific research could shed some light on this. Indeed, if the effectiveness of total containment is scientifically proven, its implementation becomes legitimate, and vice versa.

It therefore becomes important to analyze the effectiveness of the total containment measure implemented during the first act of the epidemic. To this end, existing work shows that, in general, its implementation would have made it possible to flatten the contamination curve. In particular, Maier and Brockmann (2020) show that total containment was effective in mainland China using a parsimonious model that countries. However, this effectiveness would be less if containment is not implemented early and if health systems are not sufficiently developed (Deb et al. 2020) .

The studies listed above analyze the effect of total population containment associated with a set of other restrictive measures on the evolution of the curve of confirmed cases in a country or group of countries without comparing the situation of these countries with that of countries that have not implemented total population containment. The originality of our analysis is to evaluate the effect of a single restrictive measure, in this case total population containment, on the evolution of confirmed covid-19 cases. To do so, a methodological approach is required that compares the treated sample where the policy was applied and the untreated sample where the policy was not applied. It therefore leads to a comparison of the evolution of confirmed covid-19 cases in countries that have applied the total population containment measure and the control country that has not applied the same measure.

In our study, we compare the situations of England, Belgium, France and Italy with that of Sweden, which did not confine its population.

To do so, we use interrupted time series method (ISTA), which is often used in the literature to assess the effectiveness of public policies (Muller 2004) , the effect of new regulations (Briesacher et al. 2013) or the effectiveness of new health technologies (Ramsay et al. 2003) . In our study, we consider this method to be suitable for assessing the effectiveness of total population containment because it allows us to calculate the difference between post-intervention changes in confirmed cases of covid-19 in countries where total population containment has been applied and changes in confirmed cases of covid-19 in the control country where total population containment has not been applied. For this purpose, we look at the statistical significance of the linear post-intervention trends of covid-19 confirmed cases. In other words, are the post-intervention linear trends of covid-19 confirmed cases that were observed during the period of total population containment in the countries where this policy was applied and in the control country where this policy was not applied statically different?

Comparison of linear post-intervention trends in covid-19 confirmed cases conveys two main messages: (i) there is no statistically significant difference between the dynamics of the growth rates of the number of covid-19 confirmed cases per day during the periods of total population containment in England, Belgium and France J o u r n a l P r e -p r o o f and the dynamics observed in Sweden during the same periods; (ii) the dynamics of the growth rate of the number of covid-19 confirmed cases per day during the period of total population containment in Italy is statistically superior to that observed in Sweden during the same period.

We model the difference in the dynamics of the growth rates of the number of confirmed covid-19 cases in England, Belgium, France and Italy following the application of total population containment in these countries, with that observed in Sweden, which did not contain its population using ITSA. Total population containment was implemented on March 24, 2020 in England, March 17 in Belgium and France, and March 10 in Italy. In the model, these dates represent the start of policy intervention. ITSA has been used extensively in the literature to analyze the effectiveness of an intervention or policy implementation. In this regard, we draw on the work of Simonton (1977a; 1977b) , Huitema and McKean (2000) , Linden and Adams (2011), Linden and Arbor (2015; 2017) :

is the growth rate of the number of confirmed cases of covid-19 at time t. represents the level of the growth rate of the number of confirmed cases of covid-19 before the application of total containment. is the time elapsed since the start of the pendemia. The coefficient that is asscociated to it gives an idea of the dynamics of in the sample countries before the application of the policy, without comparison with the control country.

is a dummy variable that takes the value 0 the period before the implementation of total population containment in each sample country and 1 during the period of containment. Z is a dummy variable that represents the control country and gives the interaction terms , and . The coefficients , , and make it possible to assess the situation of confirmed cases of covid-19 before the total containment of the population in the countries of the sample without comparison with the control country. On the other hand, the coefficients , , and allow the situation to be assessed in comparison with the control country. Thus, the coefficient represents the difference in the constant, between the growth rate of confirmed cases of covid-19 in the country where total population containment was applied and in the control country where this measure was not applied. The coefficient represents the difference in the slope (trend), between the growth rate of confirmed covid-19 cases prior to the application of total containment, comparing the sample countries and Sweden which did not apply total population containment. The coefficient represents the difference in the level of the growth rate of confirmed covid-19 cases, comparing the sample countries and Sweden on the first day of containment. Finally, represents the difference in the slope (trend) of the growth rates of confirmed covid-19 cases, comparing the sample countries and Sweden, during the period of total population containment. In relation to the object of study of this work, it is the sign and statistical significance of the comparison of the linear post-intervention trends, noted "Difference" in Table 1 , that allow us to conclude whether or not the measure of total population containment is effective. The data are taken from the European Centre for Disease Prevention and Control website 1 .

The results are presented in Table 1 and in graphical form (see Figure 1 ). As explained earlier, it is the sign and statistical significance of the coefficient of "Difference" in Table 1 that tells us whether or not the total containment of the population was effective. If the sign of the coefficient is negative and significant, the situation has improved more in the country that has implemented the policy, compared with the situation in Sweden, and vice versa if the sign is positive and significant. On the other hand, if the coefficient is not significant, the situation in both countries remained the same during the period of total population containment, regardless of the sign of the coefficient. Thus, in order to have an overall appreciation of the comparative effect of total population containment on the dynamics of growth rates of confirmed covid-19 cases, we look at the statistical significance of the estimated coefficients of 1 https://www.ecdc.europa.eu/en/publications-data/download-todays-data-geographic-distribution-covid-19-cases-worldwide J o u r n a l P r e -p r o o f "Difference", which allows us to analyze the statistical significance of the comparison of post-intervention linear trends. In this regard, there is no statistically significant difference between the post-intervention linear trends in England, Belgium and

France during the periods of total population containment in these countries, and that observed in Sweden during the same periods. In addition, the difference in the post-intervention linear trends for Italy and Sweden is positive and statistically significant at an error probability of less than 10%. This means that, despite the implementation of total population containment in Italy, the dynamics of the growth rate of confirmed covid-19 cases in that country was higher than that observed in Sweden, a country that had not applied the same policy. These results complement the existing literature on the effectiveness of total population containment. Indeed, while existing work shows that the curve of confirmed cases of covid-19 flattens during the period of total containment (Maier and Brockmann, 2020; Wong et al. 2020) , especially if the latter is applied very early (Deb et al. 2020) , our results show that even if there may be some flattening of the curve, this is not necessarily due to total population containment, as the same is observed in the control country that did not apply the same policy. Worse, there is even a worsening of the situation in Italy, compared to Sweden. To fully appreciate this lack of difference between the confined countries and Sweden, we present the results in Table 1 graphically below. 

Total population containment has been implemented in many countries impacted by covid-19 in order to contain the spread of the virus. An analysis of the situation in Belgium, England, France and Italy, countries that have implemented this policy, does not allow concluding its effectiveness when comparing their situations with that of Sweden, which has not contained its population. 

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