The use of the dynamic time warping (DTW) method to describe the COVID-19 dynamics in Poland
DOI:
https://doi.org/10.24136/oc.2021.018Keywords:
COVID-19, coronavirus, regional analysis, dynamic time warping, clusteringAbstract
Research background: In recent times, the whole world has been severely affected by the COVID-19 pandemic. The influence of the epidemic on the society and the economy has caused a great deal of scientific interest. The development of the pandemic in many countries was analyzed using various models. However, the literature on the dissemination of COVID-19 lacks econometric analyzes of the development of this epidemic in Polish voivodeships.
Purpose of the article: The aim of the study is to find similarities in time series for infected with and those who died of COVID-19 in Polish voivodeships using the method of dynamic time warping.
Methods: The dynamic time warping method allows to calculate the distance between two time series of different lengths. This feature of the method is very important in our analysis because the coronavirus epidemic did not start in all voivodeships at the same time. The dynamic time warping also enables an adjustment of the timeline to find similar, but shifted, phases. Using this method, we jointly analyze the number of infected and deceased people in each province. In the next step, based on the measured similarity of the time series, the voivodeships are grouped hierarchically.
Findings & value added: We use the dynamic time warping to identify groups of voivodeships affected by the epidemic to a different extent. The classification performed may be useful as it indicates patterns of the COVID-19 disease evolution in Polish voivodeships. The results obtained at the regional level will allow better prediction of future infections. Decision makers should formulate further recommendations for lockdowns at the local level, and in the long run, adjust the medical infrastructure in the regions accordingly. Policymakers in other countries can benefit from the findings by shaping their own regional policies accordingly.
Downloads
References
Aldridge, R. W., Lewer, D., Katikireddi, S. V., Mathur, R., Pathak, N., Burns, R., Fragaszy, E. B., Johnson, A. M., Devakumar, D., Abubakar, I., & Hayward, A. (2020). Black, Asian and minority ethnic groups in England are at increased risk of death from Covid-19: indirect standardisation of NHS mortality data. Wellcome Open Research, 5(88). doi: 10.12688/wellcomeopenres.15922.2. DOI: https://doi.org/10.12688/wellcomeopenres.15922.1
View in Google Scholar
Anastassopoulou, C., Russo, L., Tsakris, A., & Siettos, C. (2020). Data-based analysis, modelling and forecasting of the COVID-19 outbreak. PLOS ONE, 15:e0230405. doi: 10.1371/journal.pone.0230405. DOI: https://doi.org/10.1371/journal.pone.0230405
View in Google Scholar
Anderson, R. M., & May, R. M. (1992). Infectious diseases of humans: dynamics and control. Oxford: Oxford University Press. doi:10.1002/hep.1840150131. DOI: https://doi.org/10.1002/hep.1840150131
View in Google Scholar
Arici, T., Celebi, S., Aydin, A. S., & Temiz, T. T. (2013). Robust gesture recognition using feature pre-processing and weighted dynamic time warping. Multimedia Tools and Applications, 72, 3045?3062. doi: 10.1007/s11042-013-1591-9. DOI: https://doi.org/10.1007/s11042-013-1591-9
View in Google Scholar
Bellman, R., & Kalaba, R. (1959). On adaptive control processes. IRE Transactions on Automatic Control, 4(2), 1?9. doi: 10.1109/TAC.1959.1104 847. DOI: https://doi.org/10.1109/TAC.1959.1104847
View in Google Scholar
Benvenuto, D., Giovanetti, M., Vassallo, L., Angeletti, S., & Ciccozzi, M. (2020). Application of the ARIMA model on the COVID-2019 epidemic dataset. Data in Brief, 29, 105340. doi: 10.1016/j.dib.2020.105340. DOI: https://doi.org/10.1016/j.dib.2020.105340
View in Google Scholar
Casella, F. (2021). Can the COVID-19 epidemic be controlled on the basis of daily test reports? IEEE Control Systems Letters, 5(3), 1079?1084. doi: 10.1109/LCS YS.2020.3009912. DOI: https://doi.org/10.1109/LCSYS.2020.3009912
View in Google Scholar
Ceylan, Z. (2020). Estimation of COVID-19 prevalence in Italy, Spain, and France. Science of The Total Environment, 729, 138817. doi: 10.1016/j.scitotenv.2020. 138817. DOI: https://doi.org/10.1016/j.scitotenv.2020.138817
View in Google Scholar
Chu, J. (2021). A statistical analysis of the novel coronavirus (COVID-19) in Italy and Spain. PLoS ONE, 16(3): e0249037. doi: 10.1371/journal.pone.0249037. DOI: https://doi.org/10.1371/journal.pone.0249037
View in Google Scholar
Czech, K., Wielechowski, M., Kotyza, P., Benešová, I., & Laputková, A. (2020). Shaking stability: COVID-19 impact on the Visegrad Group countries? financial markets. Sustainability,12, 6282. doi: 10.3390/su12156282. DOI: https://doi.org/10.3390/su12156282
View in Google Scholar
Giorgino, T. (2009). Computing and visualizing dynamic time warping alignments in R: the dtw package. Journal of Statistical Software, 31(7), 1?24. doi: 10.186 37/jss.v031.i07. DOI: https://doi.org/10.18637/jss.v031.i07
View in Google Scholar
Jarynowski, A., Wójta-Kempa, M., & Krzowski, Ł. (2020a). An attempt to optimize human resources allocation based on spatial diversity of COVID-19 cases in Poland. medRxiv preprint. doi: 10.1101/2020.10.14.20090985. DOI: https://doi.org/10.1101/2020.10.14.20090985
View in Google Scholar
Jarynowski, A., Wójta-Kempa, M., Płatek, D., & Czopek, K. (2020b). Attempt to understand public-health relevant social dimensions of COVID-19 outbreak in Poland. Society Register, 4(3), 7?44. doi: 10.14746/sr.2020.4.3.01. DOI: https://doi.org/10.14746/sr.2020.4.3.01
View in Google Scholar
Keogh, E., & Ratanamahatana, C. A. (2005). Exact indexing of dynamic time warping. Knowledge and Information Systems, 7, 358?386. doi: 10.1007/s1011 5-004-0154-9. DOI: https://doi.org/10.1007/s10115-004-0154-9
View in Google Scholar
Kochanczyk, M., Grabowski, F., & Lipniacki, T. (2020). Dynamics of COVID-19 pandemic at constant and time-dependent contact rates. Mathematical Modelling of Natural Phenomena, 15(28). doi: 10.1051/mmnp/2020011. DOI: https://doi.org/10.1051/mmnp/2020011
View in Google Scholar
Korzeb, Z., & Niedziółka, P. (2020). Resistance of commercial banks to the crisis caused by the COVID-19 pandemic: the case of Poland. Equilibrium. Quarterly Journal of Economics and Economic Policy, 15(2), 205?234. doi: 10.24136/eq. 2020.010. DOI: https://doi.org/10.24136/eq.2020.010
View in Google Scholar
Krywyk, J., Oettgen, W., Messier, M., Mulot, M., Ugon, A., & Toubiana, L. (2020). Dynamics of the COVID-19 pandemics: global pattern and between countries variations. medRxiv preprint. doi: 10.1101/2020.07.20.20155390. DOI: https://doi.org/10.1101/2020.07.20.20155390
View in Google Scholar
Kufel, T. (2020). ARIMA-based forecasting of the dynamics of confirmed COVID-19 cases for selected European countries. Equilibrium. Quarterly Journal of Economics and Economic Policy, 15(2), 181?204. doi: 10.24136/eq. 2020.009. DOI: https://doi.org/10.24136/eq.2020.009
View in Google Scholar
Kumar, P., Kalita, H., Patairiya, S., Sharma, Y. D., Nanda, C., Rani, M., Rahmani, J., & Bhagavathula, A. S. (2020). Forecasting the dynamics of COVID-19 pandemic in top 15 countries in April 2020: ARIMA model with machine learning approach. medRxiv preprint. doi: 10.1101/2020. 03.30.20046227. DOI: https://doi.org/10.1101/2020.03.30.20046227
View in Google Scholar
Landmesser, J. (2021). Analysis of COVID-19 dynamics in EU countries using the dynamic time warping method and ARIMA Models. In K. Jajuga, K. Najman, & M. Walesiak (Eds.). Data analysis and classification. Methods and applications. Springer International Publishing. 337?352. doi:10.1007/978-3-030-75190-6_19. DOI: https://doi.org/10.1007/978-3-030-75190-6_19
View in Google Scholar
Lin, Q., Zhao, S., Gao, D., Lou, Y., Yang, S., Musa, S. S., Wang, M. H., Cai, Y., Wang, W., Yang, L., & He, D. (2020). A conceptual model for the coronavirus disease 2019 (COVID-19) outbreak in Wuhan, China with individual reaction and governmental action. International Journal of Infectious Diseases, 93, 211?216. doi: 10.1016/j.ijid.2020.02.058. DOI: https://doi.org/10.1016/j.ijid.2020.02.058
View in Google Scholar
Müller, M. (2007). Information retrieval for music and motion. Springer-Verlag Berlin Heidelberg. doi: 10.1007/978-3-540-74048-3. DOI: https://doi.org/10.1007/978-3-540-74048-3
View in Google Scholar
Orzechowska, M., & Bednarek, A. K. (2020). Forecasting COVID-19 pandemic in Poland according to government regulations and people behavior. medRxiv preprint. doi: 10.1101/2020.05.26.20112458. DOI: https://doi.org/10.1101/2020.05.26.20112458
View in Google Scholar
Pardal, P., Dias, R., Šuleř, P., Teixeira, N., & Krulický, T. (2020). Integration in Central European capital markets in the context of the global COVID-19 pandemic. Equilibrium. Quarterly Journal of Economics and Economic Policy, 15(4), 627?650. doi: 10.24136/eq.2020.027. DOI: https://doi.org/10.24136/eq.2020.027
View in Google Scholar
Rabiner, L., Rosenberg, A., & Levinson, S. (1978). Considerations in dynamic time warping algorithms for discrete word recognition. IEEE Transactions Acoustic Speech Signal Process, 26(6), 575?582. doi: 10.1109/tassp.1978.116 3164. DOI: https://doi.org/10.1109/TASSP.1978.1163164
View in Google Scholar
Raciborski, F., Pinkas, J., Jankowski, M., Sierpiński, R. A., Zgliczyński, W. S., Szumowski, Ł., Rakocy, K., Wierzba, W., & Gujski, M. (2020). Dynamics of the coronavirus disease 2019 outbreak in Poland: an epidemiological analysis of the first 2 months of the epidemic. Polish Archives of Internal Medicine, 130(7-8), 615?621. doi: 10.20452/pamw.15430. DOI: https://doi.org/10.20452/pamw.15430
View in Google Scholar
Rogalski, M. (2021). COVID-19 w Polsce. Retrieved from http://bit.ly/covid19-poland (15.01.2021).
View in Google Scholar
Rojas, F., Valenzuela, O., & Rojas, I. (2020). Estimation of COVID-19 dynamics in the different states of the United States using time-series clustering. medRxiv preprint. doi: 10.1101/2020.06.29.20142364. DOI: https://doi.org/10.1101/2020.06.29.20142364
View in Google Scholar
Roques, L., Klein, E. K., Papaix, J., Sar, A., & Soubeyrand, S. (2020). Using early data to estimate the actual infection fatality ratio from COVID-19 in France. Biology, 9(5), 97. doi: 10.3390/biology9050097. DOI: https://doi.org/10.3390/biology9050097
View in Google Scholar
Sakoe, H., & Chiba, S. (1978). Dynamic programming algorithm optimization for spoken word recognition. IEEE Transactions on Acoustics, Speech, and Signal Processing, 26(1), 43?49. doi: 10.1109/tassp.1978.1163055. DOI: https://doi.org/10.1109/TASSP.1978.1163055
View in Google Scholar
Sardá-Espinosa, A. (2019). Time-series clustering in R using the dtwclust package. R Journal, 11(1), 22?43. doi: 10.32614/RJ-2019-023. DOI: https://doi.org/10.32614/RJ-2019-023
View in Google Scholar
Statista (2021). Coronavirus (COVID-19) in Poland. Retrieved from https://www.statista.com/study/71486/coronavirus-covid-19-in-poland/ (15.01.2021).
View in Google Scholar
Stübinger, J. (2019). Statistical arbitrage with optimal causal paths on high-frequency data of the S&P 500. Quantitative Finance, 19, 921?935. doi: 10.10 80/14697688.2018.1537503. DOI: https://doi.org/10.1080/14697688.2018.1537503
View in Google Scholar
Stübinger, J., & Schneider, L. (2020). Epidemiology of coronavirus COVID-19: forecasting the future incidence in different countries. Healthcare, 8(2), 99. doi: 10.3390/healthcare8020099. DOI: https://doi.org/10.3390/healthcare8020099
View in Google Scholar
Svabova, L., Tesarova, E. N., Durica, M., & Strakova, L. (2021). Evaluation of the impacts of the COVID-19 pandemic on the development of the unemployment rate in Slovakia: counterfactual before-after comparison. Equilibrium. Quarterly Journal of Economics and Economic Policy, 16(2), 261?284. doi: 10.24136/eq.2021.010. DOI: https://doi.org/10.24136/eq.2021.010
View in Google Scholar
Wielechowski, M., Czech, K., & Grzęda, Ł. (2020). Decline in mobility: public transport in Poland in the time of the COVID-19 pandemic. Economies, 8(4), 78. doi: 10.3390/economies8040078. DOI: https://doi.org/10.3390/economies8040078
View in Google Scholar
Worldometer (2021). COVID-19 coronavirus pandemic. Retrieved from https://www.worldometers.info/coronavirus/ (30.01.2021).
View in Google Scholar
Zinecker, M., Doubravský, K., Balcerzak, A. P., Pietrzak, M. B., & Dohnal, M. (2021). The Covid-19 disease and policy response to mitigate the economic impact in the EU: an exploratory study based on qualitative trend analysis. Technological and Economic Development of Economy, 27(3), 742?762. doi: 10.3846/tede.2021.14585. DOI: https://doi.org/10.3846/tede.2021.14585
View in Google Scholar
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Oeconomia Copernicana
This work is licensed under a Creative Commons Attribution 4.0 International License.