A Transnational and Transregional Study of the Impact and Effectiveness of Social Distancing for COVID-19 Mitigation
<p>Social distancing metric <span class="html-italic">M</span> in Equation (<a href="#FD5-entropy-23-01530" class="html-disp-formula">5</a>) for (<b>A</b>) Brazil states and (<b>B</b>) USA states.</p> "> Figure 2
<p>(<b>A</b>) Time variation of <math display="inline"><semantics> <mrow> <mover> <mi>β</mi> <mo>¯</mo> </mover> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </semantics></math> and <math display="inline"><semantics> <msub> <mi>R</mi> <mi>t</mi> </msub> </semantics></math> for Los Angeles county. (<b>B</b>) Spearman’s rank-order correlation <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>s</mi> </msub> <mrow> <mo>[</mo> <mi>M</mi> <mo>,</mo> <mover> <mi>β</mi> <mo>¯</mo> </mover> <mo>]</mo> </mrow> </mrow> </semantics></math> between the social distancing metric <span class="html-italic">M</span> and the infection rate <math display="inline"><semantics> <mover> <mi>β</mi> <mo>¯</mo> </mover> </semantics></math> and <math display="inline"><semantics> <mrow> <msub> <mi>r</mi> <mi>s</mi> </msub> <mrow> <mo>[</mo> <mi>M</mi> <mo>,</mo> <msub> <mi>R</mi> <mi>t</mi> </msub> <mo>]</mo> </mrow> </mrow> </semantics></math> between <span class="html-italic">M</span> and the effective reproduction number <math display="inline"><semantics> <msub> <mi>R</mi> <mi>t</mi> </msub> </semantics></math> for Los Angeles county in the United States.</p> "> Figure 3
<p>Spearman’s correlation index <math display="inline"><semantics> <msub> <mi>r</mi> <mi>s</mi> </msub> </semantics></math> between the social distancing metric <span class="html-italic">M</span> and the infection rate <math display="inline"><semantics> <mover> <mi>β</mi> <mo>¯</mo> </mover> </semantics></math> for: (<b>A</b>) Brazilian states; (<b>B</b>) Main Brazilian municipalities with population over 750 thousand; (<b>C</b>) 22 European countries; (D) US counties with at least one million inhabitants. (<b>D</b>) Main counties in the United States. Bar colors give the proportion of days with a mask mandate since the beginning of the pandemic in each location, up to 20 December 2020; (<b>E</b>) same as (<b>D</b>) but considering only the period with a mask mandate. States without a mask mandate in the period considered are marked in black. (<b>F</b>) Same as (<b>D</b>) but for all American states. (<b>G</b>) Same as (<b>E</b>) but for the American states.</p> "> Figure 4
<p>Spearman’s correlation index <math display="inline"><semantics> <msub> <mi>r</mi> <mi>s</mi> </msub> </semantics></math> between each mobility variable and the infection rate <math display="inline"><semantics> <mover> <mi>β</mi> <mo>¯</mo> </mover> </semantics></math> for the main Brazilian municipalities, each Brazilian state and European countries.</p> "> Figure 5
<p>Spearman’s correlation index <math display="inline"><semantics> <msub> <mi>r</mi> <mi>s</mi> </msub> </semantics></math> between changes in each mobility category and the infection rate <math display="inline"><semantics> <mover> <mi>β</mi> <mo>¯</mo> </mover> </semantics></math> for (<b>A</b>) counties with more than one million inhabitants and one thousand deaths for the period from the first COVID-19 case up to 20 December 2020; (<b>B</b>) same as (<b>A</b>) but for the period with a mask mandate, except those counties with no mask mandate in 2020 (marked in black in <a href="#entropy-23-01530-f003" class="html-fig">Figure 3</a>E), for which the whole period is considered; (<b>C</b>) same as (<b>A</b>) for all US states; (<b>D</b>) same as (<b>B</b>) for all US states.</p> "> Figure 6
<p>Total number of deaths per 100 thousand inhabitants at the end of the considered period as a function of the average value of <math display="inline"><semantics> <mrow> <mover> <mi>β</mi> <mo>¯</mo> </mover> <mo>/</mo> <mi>γ</mi> </mrow> </semantics></math> during the same time span.</p> "> Figure 7
<p>Coefficient <math display="inline"><semantics> <mrow> <mover> <mi>β</mi> <mo>¯</mo> </mover> <mo>/</mo> <mi>γ</mi> <mi>M</mi> <mo>=</mo> <mi>α</mi> <mo>/</mo> <mi>γ</mi> </mrow> </semantics></math> for (<b>A</b>) Brazilian states; (<b>B</b>) Brazilian municipalities; (<b>C</b>) US states; (<b>D</b>) US counties and (<b>E</b>) European countries. The normalized histogram (in red) and the log-normal distribution function (in black) for the values for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>/</mo> <mi>γ</mi> </mrow> </semantics></math>: (<b>F</b>) Brazilian states; (<b>G</b>) Brazilian municipalities, (<b>H</b>) US states; (<b>I</b>) US counties and (<b>J</b>) European countries. The values for <math display="inline"><semantics> <mrow> <mi>α</mi> <mo>/</mo> <mi>γ</mi> </mrow> </semantics></math> (CI <math display="inline"><semantics> <mrow> <mn>95</mn> <mo>%</mo> </mrow> </semantics></math>) are <math display="inline"><semantics> <mrow> <mn>0.015</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mn>0.0096</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mn>0.023</mn> </mrow> </semantics></math>), <math display="inline"><semantics> <mrow> <mn>0.019</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mn>0.0081</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mn>0.042</mn> </mrow> </semantics></math>), <math display="inline"><semantics> <mrow> <mn>0.014</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mn>0.0089</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mn>0.021</mn> </mrow> </semantics></math>), <math display="inline"><semantics> <mrow> <mn>0.015</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mn>0.0091</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mn>0.027</mn> </mrow> </semantics></math>) and <math display="inline"><semantics> <mrow> <mn>0.014</mn> </mrow> </semantics></math> (<math display="inline"><semantics> <mrow> <mn>0.0084</mn> </mrow> </semantics></math>–<math display="inline"><semantics> <mrow> <mn>0.024</mn> </mrow> </semantics></math>), respectively.</p> ">
Abstract
:1. Introduction
2. Material and Methods
2.1. Effective Reproduction Number
2.2. Infection Rate
2.3. Social Distancing Metric
2.4. Spearman’s Rank-Order Correlation
2.5. Data Sources
- Population by age for Europe: World Population Prospects—United Nations—Available online: https://population.un.org/wpp (accessed on 4 September 2021).
- Time series of deaths and cases by country: World Health Organization—Available online: https://www.who.int/emergencies/diseases/novel-coronavirus-2019 (accessed on 4 September 2021).
- Time series of cases and deaths by US counties and states: New York Times COVID-19 Tracker dataset—Available online: https://raw.githubusercontent.com/nytimes/covid-19-data/master/us-counties.csv (accessed on 4 September 2021).
- Population by age group in US counties and states: United States Census Bureau—Available online: https://www.census.gov/data/tables/time-series/demo/popest/2010s-counties-detail.html (accessed on 4 September 2021).
- Data on days of mask mandate in the US: Center for Disease Control and Prevention—Available online: https://data.cdc.gov/Policy-Surveillance/U-S-State-and-Territorial-Public-Mask-Mandates-Fro/62d6-pm5i (accessed on 4 September 2021).
- Population by age group for Brazilian municipalities and states: Brazilian Institute for Geography and Statistics—Available online: https://brasilemsintese.ibge.gov.br/populacao (accessed on 4 September 2021).
- Time series for cases and deaths by COVID-19 by municipality and state in Brazil: Brazilian Ministry of Health—Available online: https://covid.saude.gov.br (accessed on 4 September 2021).
- Detailed data on vaccination in Brazil: Brazilian Ministry of Health—Available online: https://opendatasus.saude.gov.br/dataset/covid-19-vacinacao (accessed on 4 September 2021).
3. Results and Discussion
- All 50 US states, from the first reported case up to 20 December 2020;
- The 24 US counties with a population of at least one million and at least 1000 deaths in 2020 (Nassau was not considered due to inconsistent data for the number of deaths), from the first reported case in each county up to 20 December 2020;
- All 27 Brazilian states, from 26 February 2020 to 14 June 2021;
- The 22 Brazilian cities (municipalities) with a population of at least 750 thousand from 26 February 2020 to 14 June 2021;
- All countries in the European Economic Community and the United Kingdom with Google Mobility data and at least one thousand deaths by COVID-19 in 2020, from 1 March 2020 to 31 December 2020, with a total of 22 countries.
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
Appendix A. Epidemiological Model
Variable | Description |
---|---|
Susceptible individuals | |
Exposed individuals (non-contagious) | |
Infected symptomatic individuals (contagious) | |
Asymptomatic symptomatic individuals (contagious) | |
Hospitalized individuals | |
Vaccinated individual with l doses with vaccine of type k without primary vaccination failure | |
Vaccinated individual with l doses with vaccine of type k with primary vaccination failure | |
Recovered individuals. | |
Individuals vaccinated per unit of time with the l-th dose of vaccine of type k. | |
Efficacy of vaccine of type k withe l doses. |
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Filho, T.M.R.; Moret, M.A.; Mendes, J.F.F. A Transnational and Transregional Study of the Impact and Effectiveness of Social Distancing for COVID-19 Mitigation. Entropy 2021, 23, 1530. https://doi.org/10.3390/e23111530
Filho TMR, Moret MA, Mendes JFF. A Transnational and Transregional Study of the Impact and Effectiveness of Social Distancing for COVID-19 Mitigation. Entropy. 2021; 23(11):1530. https://doi.org/10.3390/e23111530
Chicago/Turabian StyleFilho, Tarcísio M. Rocha, Marcelo A. Moret, and José F. F. Mendes. 2021. "A Transnational and Transregional Study of the Impact and Effectiveness of Social Distancing for COVID-19 Mitigation" Entropy 23, no. 11: 1530. https://doi.org/10.3390/e23111530