Spatial analysis of COVID-19 spread in Europe using "center of gravity" concept

: pp. 130–142
Received: August 28, 2021
Accepted: February 04, 2022

Mathematical Modeling and Computing, Vol. 9, No. 1, pp. 130–142 (2022)

Lviv Polytechnic National University
Lviv Polytechnic National University; WSB University, Dąbrowa Górnicza, Poland

The COVID-19 global pandemic has affected all countries and become a real challenge for humanity.  Scientists are intensively studying the specifics of the disease caused by this virus and the impact of restrictive measures on the economy, environment and other aspects of life.  We present an approach to spatial modeling and analysis of the COVID-19 spreading process using the concept of the "center of gravity".  Based on weekly data on this disease in all European countries, the trajectories of the center of gravity of new cases and deaths during the pandemic have been calculated.  These two trajectories reflect the dominant role of certain countries or regions of Europe during different stages of the pandemic.  It is shown that the amplitude of the trajectory of the center of gravity in the longitudinal direction was quite high (about 1,500 km) in comparison with the amplitude of the trajectory in the latitudinal direction (500 km).  Using an approximation of the weekly data, the delays between the peaks of new cases and mortality for different countries were calculated, as well as the delays in comparison with the countries that first reached the peaks of morbidity and mortality.  The trajectories of the center of gravity are also calculated for the regions of Ukraine as an example of analysis at the national scale.  These results provide an opportunity to understand the spatial specifics of the spread of COVID-19 on the European continent and the roles of separate countries in these complex processes.

  1. Worldometer: COVID-19 coronavirus pandemic, 2021.
  2. Azure Open Datasets Catalog: COVID-19 Data Lake, 2021.
  3. Zhang X., Ma R., Wang L.  Predicting turning point, duration and attack rate of COVID-19 outbreaks in major Western countries.  Chaos, Solitons & Fractals.  135, 109829 (2020).
  4. Zivkovic M., Bacanin N., Venkatachalam K., Nayyar A., Djordjevic A., Strumberger I., Al-Turjman F.  COVID-19 cases prediction by using hybrid machine learning and beetle antennae search approach.  Sustainable Cities and Society.  66, 102669 (2021).
  5. Kim J., Kwon O.  A model for rapid selection and COVID-19 prediction with dynamic and imbalanced data.  Sustainability.  13 (6), 3099 (2021).
  6. Vyklyuk Y., Manylich M., Škoda M., Radovanović M. M., Petrović M. D.  Modeling and analysis of different scenarios for the spread of COVID-19 by using the modified multi-agent systems – Evidence from the selected countries.  Results in Physics.  20, 103662 (2021).
  7. Tuli S., Tuli S., Tuli R., Gill S. S.  Predicting the growth and trend of COVID-19 pandemic using machine learning and cloud computing.  Internet of Things.  11, 100222 (2020).
  8. Yakovyna V., Shakhovska N.  Modelling and predicting the spread of COVID-19 cases depending on restriction policy based on mined recommendation rules.  Mathematical Biosciences and Engineering. 18 (3), 2789–2812 (2021).
  9. Basu S., Campbell R. H.  Going by the numbers: Learning and modeling COVID-19 disease dynamics.  Chaos, Solitons & Fractals.  138, 110140 (2020).
  10. Siddique A., Shahzad A., Lawler J., Mahmoud K. A., Lee D. S., Ali N., Bilal M., Rasool K.  Unprecedented environmental and energy impacts and challenges of COVID-19 pandemic.  Environmental Research.  193, 110443 (2021).
  11. Kim M. H., Kim J. H., Lee K., Gim G.-Y.  The prediction of COVID-19 using LSTM algorithms.  International Journal of Networked and Distributed Computing.  9 (1), 19–24 (2021).
  12. Morgan A. K., Awafo B. A., Quartey T.  The effects of COVID-19 on global economic output and sustainability: evidence from around the world and lessons for redress.  Sustainability: Science, Practice and Policy.  17 (1), 77–81 (2021).
  13. Kano T., Yasui K., Mikami T., Asally M., Ishiguro A.  An agent-based model of the interrelation between the COVID-19 outbreak and economic activities.  Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.  477 (2245), 20200604 (2021).
  14. Jiang P., Van Fan Y., Klemeš J. J.  Impacts of COVID-19 on energy demand and consumption: Challenges, lessons and emerging opportunities.  Applied Energy.  285, 116441 (2021).
  15. Ciais P., Bréon F.-M., Dellaert S., Wang Y., Tanaka K., Gurriaran L., Franзoise Y., Davis S., Hong C., Penuelas J., Janssens I., Obersteiner M., Deng Z., Liu Z.  Impact of lockdowns and winter temperatures on natural gas consumption in Europe.  Earth's Future.  10, e2021EF002250 (2021).
  16. Werth A., Gravino P., Prevedello G.  Impact analysis of COVID-19 responses on energy grid dynamics in Europe.  Applied Energy.  281, 116045 (2021).
  17. Straka W., Kondragunta S., Wei Z., Zhang H., Miller S. D., Watts A.  Examining the economic and environmental impacts of COVID-19 using Earth observation data.  Remote Sensing.  13 (1), 5 (2021).
  18. Levelt P. F., Zweers D. C. S., Aben I., Bauwens M., Borsdorff T., De Smedt I., Eskes H. J., Lerot C., Loyola D. G., Romahn F., Stavrakou T., Theys N., Van Roozendael M., Veefkind J. P., Verhoelst T.  Air quality impacts of COVID-19 lockdown measures detected from space using high spatial resolution observations of multiple trace gases from Sentinel-5P/TROPOMI.  Atmospheric Chemistry and Physics Discussions. 2021, 1–53 (2021).
  19. Ghosh T., Elvidge C. D., Hsu F.-C., Zhizhin M., Bazilian M.  The dimming of lights in India during the COVID-19 pandemic.  Remote Sensing.  12 (20), 3289 (2020).
  20. Yusup Y., Ramli N. K., Kayode J. S., Yin C. S., Hisham S., Isa H. M., Ahmad M. I.  Atmospheric carbon dioxide and electricity production due to lockdown.  Sustainability.  12 (22), 9397 (2020).
  21. Le Quéré C., Jackson R. B., Jones M. W., Smith A. J. P., Abernethy S., Andrew R. M., De-Gol A. J., Willis D. R., Shan Y., Canadell J. G., Friedlingstein P., Creutzig F., Peters G. P.  Temporary reduction in daily global CO2 emissions during the COVID-19 forced confinement.  Nature Climate Change.  10, 647–653 (2020).
  22. Liu Z., Ciais P., Deng Z., Davis S. J., Zheng B., Wang Y., Cui D., Zhu B., Dou X., Ke P., Sun T., Guo R., Zhong H., Boucher O., Bréon F.-M., Lu C., Guo R., Xue J., Boucher E., Tanaka K., Chevallier F. Carbon Monitor, a near-realtime daily dataset of global CO2 emission from fossil fuel and cement production.  Scientific Data.  7, 392 (2020).
  23. Liu Z., Ciais P., Deng Z., Lei R., Davis S. J., Feng S., Zheng B., Cui D., Dou X., Zhu B., Guo R., Ke P., Sun T., Lu C., He P., Wang Y., Yue X., Wang Y., Lei Y., Zhou H., Cai Z., Wu Y., Guo R., Han T., Xue J., Boucher O., Boucher E., Chevallier F., Tanaka K., Wei Y., Zhong H., Kang C., Zhang N., Chen B., Xi F., Liu M., Bréon F.-M., Lu Y., Zhang Q., Guan D., Gong P., Kammen D. M., He K., Schellnhuber H.J. Near-real-time monitoring of global CO2 emissions reveals the effects of the COVID-19 pandemic.  Nature Communications.  11, 5172 (2020).
  24. Liu Z., Deng Z., Ciais P., Tan J., Zhu B., Davis S. J, Andrew R., Boucher O., Arous S. B., Canadell P., Dou X., Friedlingstein P., Gentine P., Guo R., Hong C., Jackson R. B., Kammen D. M., Ke P., Le Quéré C., Monica C., Janssens-Maenhout G., Peters G., Tanaka K., Wang Y., Zheng B., Zhong H., Sun T., Schellnhuber H. J.  Global daily CO2 emissions for the year 2020. Preprint arXiv:2103.02526 (2021).
  25. Liu Z., Zhu B., Ciais P., Davis S. J., Lu C., Zhong H., Ke P., Cui Y., Deng Z., Cui D., Sun T., Dou X., Tan J., Guo R., Zheng B., Tanaka K., Zhao W., Gentine P.  De-carbonization of global energy use during the COVID-19 pandemic.  Preprint arXiv:2102.03240 (2021).
  26. Zeng N., Han P., Liu D., Liu Z., Oda T., Martin C., Liu Z., Yao B., Sun W., Wang P., Cai Q., Dickerson R., Maksyutov S.  Global to local impacts on atmospheric CO2 caused by COVID-19 lockdown. Preprint arXiv:2010.13025 (2020).
  27. Weir B., Crisp D., O'Dell C. W., Basu S., Chatterjee A., Oda T., Ott L. E., Pawson S., Poulter B., Zhang Z., Ciais P., Davis S. J., Liu Z.  Regional impacts of COVID-19 on carbon dioxide detected worldwide from space.  Science Advances.  7 (45), eabf9415 (2020).
  28. Wang Y., Deng Z., Ciais P., Liu Z., Davis S. J., Gentine P., Lauvaux T., Ge Q.  Transportation CO2 emissions stayed high despite recurrent COVID outbreaks.  Scientific Data.  7, 168 (2020).
  29. Han P., Cai Q., Oda T., Zeng N., Shan Y., Lin X., Liu D.  Assessing the recent impact of COVID-19 on carbon emissions from China using domestic economic data.  Science of The Total Environment.  750, 141688 (2021).
  30. Laughner J. L., Neu J. L., Schimel D., Wennberg P. O., Barsanti K., Bowman K., Chatterjee A., Croes B., Fitzmaurice H., Henze D., Kim J., Kort E. A., Liu Z., Miyazaki K., Turner A. J., Anenberg S., Avise J., Cao H., Crisp D., de Gouw J., Eldering A., Fyfe J. C., Goldberg D. L., Gurney K. R., Hasheminassab S., Hopkins F., Ivey C. E., Jones D. B. A., Lovenduski N. S., Martin R. V., McKinley G. A., Ott L., Poulter B., Ru M., Sander S. P., Swart N., Yung Y. L., Zeng Z.-C.  The 2020 COVID-19 pandemic and atmospheric composition: back to the future.  Earth and Space Science Open Archive. 11 (2021).
  31. Oda T., Haga C., Hosomi K., Matsui T., Bun R.  Errors and uncertainties associated with the use of unconventional activity data for estimating CO2 emissions.  Environmental Research Letters.  16 (8), 084058 (2021).
  32. Gurney K. R., Liang J., Patarasuk R., Song Y., Huang J., Roest G.  The Vulcan version 3.0 high-resolution fossil fuel CO2 emissions for the United States.  Journal of Geophysical Research: Atmospheres. 125 (19), e2020JD032974 (2020).
  33. Asimov I.  Understanding Physics.  Buccaneer Books, New York (1988).
  34. Levi M.  The Mathematical Mechanic: Using Physical Reasoning to Solve Problems.  Princeton University Press (2012).
  35. Chohan U. M.  The political economy of OBOR and the global economic center of gravity.  In: The Belt and Road Initiative, Chaisse J. and Górski J., eds.  Brill & Nijhoff. 59–82 (2018).
  36. Roe M. J., Coan T. G.  Financial markets and the political center of gravity.  Journal of Law, Finance, and Accounting.  2 (1), 125–171 (2017).
  37. Baltagi B. H., Egger P. H., Erhardt K.  The estimation of gravity models in international trade.  In: The Econometrics of Multi-Dimensional Panels, Matyas L., ed. 323–348 (2017).
  38. Ferwerda J., Kattenberg M., Chang H.-H., Unger B., Groot L., Bikker J. A.  Gravity models of trade-based money laundering.  Applied Economics.  45 (22), 3170–3182 (2013).
  39. Walker J., Unger B.  Measuring global money laundering: "The Walker gravity model".  Review of Law and Economics.  5 (2), 821–853 (2009).
  40. Balsa-Barreiro J., Li Y., Morales A., Pentland A.  Globalization and the shifting centers of gravity of world's human dynamics: Implications for sustainability.  Journal of Cleaner Production.  239, 117923 (2019).
  41. Li H., Song Y., Zhang M.  Study on the gravity center evolution of air pollution in Yangtze river delta of China.  Natural Hazards.  90, 1447–1459 (2018).
  42. Chen J., Xu C., Li K., Song M.  A gravity model and exploratory spatial data analysis of prefecture-scale pollutant and CO2 emissions in China.  Ecological Indicators.  90, 554–563 (2018).
  43. Song Y., Zhang M.  Study on the gravity movement and decoupling state of global energy-related CO2 emissions.  Journal of Environmental Management.  245, 302–310 (2019).
  44. Grether J.-M., Mathys N. A.  The Coronavirus Center of Gravity (CCG), 2021.
  45. Grether J.-M., Lutzelschwab C., Mathys N. A.  L'essor et le déclin de l'Occident : une perspective géographique.  Revue d'économie du développement.  20 (2), 31–56 (2012).
  46. DIVA-GIS:  Free Spatial Data (2021).