COVID-19 pandemisinin farklı ülkelerdeki zamana bağlı entropi değişimine dayalı istatistiksel analizi
Abstract
Amaç: Covid-19 pandemisinin Dünya üzerinde ilerlemesindeki davranışlarını anlama konusunda büyük bir beklenti ile farklı epidemiyolojik modeller kullanılarak çalışmalar yapılmaktadır. Pandeminin yayılmasındaki düzensizlik seviyeleri arasında bir karşılaştırma yapmak, ülkelerelin pandemiye karşı toplumsal reaksiyonu, sosyo-ekonomik yapıları ve sağlık sistemleri hakkında da bilgi verebilir. Yöntem: Bu çalışmada, entropik ölçüt kullanarak Covid-19 pandemisinin istatistiksel analizini yapılmaktadır. Bunun için, günlük vaka sayılarınan oluşturulan verilere Boltzmann-Gibbs-Shannon (BGS) entropi metodu uygulanarak, Covid-19 pandemisinin entropik davranışına göre düzensizliği ve öngörülebilirliği belirlenmektedir. Birleşik Krallık, Almanya, Fransa, İtalya ve İspanya, Türkiye, Rusya ve İran’da pandemi başlangıcından 29 Ağustos 2021 tarihine kadar gerçekleşen günlük vaka sayıları, haftalık gruplara ayrılarak BGS entropi değerleri hesaplanmakta ve bu ülkeler pandemi yayılımının öngörülebilirliği konusunda sınıflandırılmaktadır. Bulgular: Pandeminin öngörülebilirliğinin beş büyük Avrupa ülkesi ile Turkiye, Rusya ve İran arasında farklılık gösterdiği tespit edilmektedir. Ayrıca, ülkelerin aşı programlarının ve 20I/501Y.V1, 20H/501.V2, 21A/S:478K, 20J/501Y.V3 varyantlarının incelenen ülkelerde pandeminin yayılmasındaki öngörülebilirliğe etki ettiği gözlenmektedir. Sonuç: BGS entropisi kullanılarak Covid-19 pandemisi günlük vaka sayılarının düzensizliğini belirlemenin, ülkeler arasında pandemi yayılımının karşılaştırmasında etkili olduğu görülmektedir ve elde edilen sonuçların pandemik sistem için epidemiyolojik modeller kullanılarak yapılan ülkelerin sınıflandırması çalışmalarında kullanılabileceği görülmektedir.
Keywords
References
- Heymann DL, Shindo N. WHO Scientific and Technical Advisory Group for Infectious Hazards. COVID-19: what is next for public health? Lancet 2020;395(10224):542-545.
- Habibi R, Burci GL, Campos TC et al. Do not violate the International Health Regulations during the COVID-19 outbreak. Lancet 2020;395(10225): 664–666.
- Corpuz JCG. Adapting to the culture of ‘new normal’: an emerging response to COVID-19. J Public Health 2021;43(2):344–345.
- Felten R, Dubois M, Ugarte-Gil MF et al. Vaccination against COVID-19: Expectations and concerns of patients with autoimmune and rheumatic diseases. Lancet Rheumatology 2021;3(4):243-245.
- Davies NG, Bernard RC, Jarvis CI et al. Association of tiered restrictions and a second lockdown with COVID-19 deaths and hospital admissions in England: a modelling study. Lancet Infect Dis 2021;21(4):482-492.
- Brookman S, Cook J, Zocherman M, Broughton S, Harman K, Gupta A. Effect of the new SARS-CoV-2 variant B.1.1.7 on children and young people. Lancet Child Adolesc Health 2021;5(4):9-10.
- Polack FP, Thomas JS, Kitchin N et al. Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine. N Engl J Med 2020;385(19):1761-1773.
- Voysey M, Clemens SAC, Madhi SA et al. Single-dose administration and the influence of the timing of the booster dose on immunogenicity and efficacy of ChAdOx1 nCoV-19 (AZD1222) vaccine: a pooled analysis of four randomised trials. Lancet 2021;397(10277):881-891.
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- Badr HS, Du H, Marshall M, Dung E, Squire MM, Gardner LM. Association between mobility patterns and COVID-19 transmission in the USA: a mathematical modelling study. The Lancet Infect Dis 2020;20(11):1247–1254.
- Chang S, Pierson E, Koh PW et al. Mobility network models of COVID-19 explain inequities and inform reopening. Nature 2020;589(7840):82-87.
- Silva JC, Contin G, Cruz C et al. Complex network model for COVID-19: human behavior, pseudo-periodic solutions and multiple epidemic waves. 2020; arXiv:2010.02368.
- Wang Z, Broccardo M, Mignan A, Sornette D. The dynamics of entropy in the COVID-19 outbreaks. Nonlinear Dyn 2020;101:1847–1869.
- Tsallis C and Tirnakli U. Predicting COVID-19 Peaks Around the World. Front Phys 2020;8:217.
- Zenk L, Steiner G, Cunha MP et al. Fast Response to Superspreading: Uncertainty and Complexity in the Context of COVID-19. Int J Environ Res Public Health 2020;17(21):7884.
- Sahin O, Salim H, Suprun E et.al. Developing a Preliminary Causal Loop Diagram for Understanding the Wicked Complexity of the COVID-19 Pandemic. Systems 2020;8(2):20.
- Salas J. Improving the estimation of the COVID-19 effective reproduction number using nowcasting. Stat Methods Med Res 2021;30(9):2075-2084.
- Zhang T, Lin G. Generalized k -means in GLMs with applications to the outbreak of COVID-19 in the United States. Comput Stat Data Anal 2021;159:107217.
- Chatzisavvasa K, Moustakidisb C, and Panosc CP. Information entropy, information distances, and complexity in atoms. J Chem Phys 2005;123(17):174111.
- Morzy M, Kajdanowicz T, and Kazienko P. On Measuring the Complexity of Networks: Kolmogorov Complexity versus Entropy. Complexity 2017;2017(3250301):1-12.
- Yılmaz N, Akilli M, Ozbek M, Zeren T, Akdeniz KG. Application of the nonlinear methods in pneumocardiogram signals. J Biol Phys 2020;46(2):209-222.
- Umberto L, Thomas DS, Giulia G. Entropy-Based Pandemics Forecasting. Front Phys 2020;8:274.
- Ghanbari A, Khordad R, Ghaderi-Zefrehei M. Mathematical prediction of the spreading rate of COVID-19 using entropy-based thermodynamic model. Indian J Phys 2021;95:2567–2573.
- Gibbs JW. Elementary Principles in Statistical Mechanics. New York: C. Scribner’s Sons,1902.
- Shannon CE. A Mathematical Theory of Communication. Bell Syst Tech J 1948;27(3):379–423.
- Jaynes ET. Information Theory and Statistical Mechanics. Phys Rev 1957;106(4):620-630.
- Penrose O. Foundations of Statistical Mechanics: A Deductive Treatment. Oxford: Pergamon, 1970.
- Gray RM. Entropy and Information Theory. Berlin: Springer, 2009.
- Beck C. Generalized information and entropy measures in physics. Contemp Phys 2009;50(4):495–510.
- Akıllı M, Yılmaz N and Akdeniz KG. Study of the q-Gaussian Distribution with the Scale Index and Calculating Entropy by Normalized Inner Scalogram. Phys Lett A 2019;383(11):1099-1104.
- Ritchie H, Mathiew E, Rodes-Guirao L et al. Coronavirus Pandemic (COVID-19) [online]. Available at: https://ourworldindata.org/coronavirus. Accessed September 2,2021.
- Gubrium N, Gubrium E. Narrative complexity in the time of COVID-19. Lancet 397(10291):2244-2245.
- Darby AC and Hiscox JA. Covid-19: variants and vaccination. BMJ 2021;372.
A statistical analysis of COVID-19 pandemic based on the temporal evolution of entropy in different countries
Abstract
Objective: Currently the Covid-19 pandemic is studied with great expectations by several epidemiological models with the aim of predicting the future behaviour of the pandemic. Determining the level of disorder in the pandemic can give us insight into the societal reactions to the pandemic the socio-economic structures and health systems in different countries. Methods: We perform a statistical analysis of Covid-19 pandemic using an entropy measure. For this, the Boltzmann-Gibbs-Shannon (BGS) entropy method is applied to the daily case data and the predictability in the covid-19 pandemic is discussed based on its entropic behaviour. The BGS entropy of the time evolution of daily cases in weekly groups from the beginning of the pandemic to 29 August 2021 in the UK, Germany, France, Italy, and Spain, Turkey, Russia and Iran are calculated and the given countries are classified by the predictability of the spread of the pandemic. Results: There is a clear difference in the predictability of the pandemic between the European countries and Turkey, Russia, and Iran. It is also observed that the vaccination programs and the Covid-19 variants of concerns; 20I/501Y.V1, 20H/501.V2, 21A/S:478K and 20J/501Y.V3 have effected the predictability of the pandemic in given countries are observed. Conclusion: The BGS entropy-based approach to determine the disorder in the time evolution of daily cases of the Covid-19 pandemic is effective and the results can be beneficial for comparison of the country classifications generated by the epidemiological models of this pandemic system.
Keywords
References
- Heymann DL, Shindo N. WHO Scientific and Technical Advisory Group for Infectious Hazards. COVID-19: what is next for public health? Lancet 2020;395(10224):542-545.
- Habibi R, Burci GL, Campos TC et al. Do not violate the International Health Regulations during the COVID-19 outbreak. Lancet 2020;395(10225): 664–666.
- Corpuz JCG. Adapting to the culture of ‘new normal’: an emerging response to COVID-19. J Public Health 2021;43(2):344–345.
- Felten R, Dubois M, Ugarte-Gil MF et al. Vaccination against COVID-19: Expectations and concerns of patients with autoimmune and rheumatic diseases. Lancet Rheumatology 2021;3(4):243-245.
- Davies NG, Bernard RC, Jarvis CI et al. Association of tiered restrictions and a second lockdown with COVID-19 deaths and hospital admissions in England: a modelling study. Lancet Infect Dis 2021;21(4):482-492.
- Brookman S, Cook J, Zocherman M, Broughton S, Harman K, Gupta A. Effect of the new SARS-CoV-2 variant B.1.1.7 on children and young people. Lancet Child Adolesc Health 2021;5(4):9-10.
- Polack FP, Thomas JS, Kitchin N et al. Safety and Efficacy of the BNT162b2 mRNA Covid-19 Vaccine. N Engl J Med 2020;385(19):1761-1773.
- Voysey M, Clemens SAC, Madhi SA et al. Single-dose administration and the influence of the timing of the booster dose on immunogenicity and efficacy of ChAdOx1 nCoV-19 (AZD1222) vaccine: a pooled analysis of four randomised trials. Lancet 2021;397(10277):881-891.
- Tregoning JS, Flight KE, Higham SL, Wang Z, Pierce BF. Progress of the COVID-19 vaccine effort: viruses, vaccines and variants versus efficacy, effectiveness and escape. Nat Rev Immunol 2021;21(10):626-636.
- Strogatz SH. Nonlinear Dynamics and Chaos. New York: CRC Press, 1994.
- Thurner S, Hanel R, and Klimek P. Introduction to the Theory of Complex Systems. New York: Oxford University Press, 2018.
- Pearce N, Merletti F. Complexity, simplicity, and epidemiology. Int J Epidemiol 2006; 35(3):515–519.
- Hufnagel L, Brockmann D, Geisel T. Forecast and control of epidemics in a globalized world. PNAS 2004;101(42):15124‐15129.
- Badr HS, Du H, Marshall M, Dung E, Squire MM, Gardner LM. Association between mobility patterns and COVID-19 transmission in the USA: a mathematical modelling study. The Lancet Infect Dis 2020;20(11):1247–1254.
- Chang S, Pierson E, Koh PW et al. Mobility network models of COVID-19 explain inequities and inform reopening. Nature 2020;589(7840):82-87.
- Silva JC, Contin G, Cruz C et al. Complex network model for COVID-19: human behavior, pseudo-periodic solutions and multiple epidemic waves. 2020; arXiv:2010.02368.
- Wang Z, Broccardo M, Mignan A, Sornette D. The dynamics of entropy in the COVID-19 outbreaks. Nonlinear Dyn 2020;101:1847–1869.
- Tsallis C and Tirnakli U. Predicting COVID-19 Peaks Around the World. Front Phys 2020;8:217.
- Zenk L, Steiner G, Cunha MP et al. Fast Response to Superspreading: Uncertainty and Complexity in the Context of COVID-19. Int J Environ Res Public Health 2020;17(21):7884.
- Sahin O, Salim H, Suprun E et.al. Developing a Preliminary Causal Loop Diagram for Understanding the Wicked Complexity of the COVID-19 Pandemic. Systems 2020;8(2):20.
- Salas J. Improving the estimation of the COVID-19 effective reproduction number using nowcasting. Stat Methods Med Res 2021;30(9):2075-2084.
- Zhang T, Lin G. Generalized k -means in GLMs with applications to the outbreak of COVID-19 in the United States. Comput Stat Data Anal 2021;159:107217.
- Chatzisavvasa K, Moustakidisb C, and Panosc CP. Information entropy, information distances, and complexity in atoms. J Chem Phys 2005;123(17):174111.
- Morzy M, Kajdanowicz T, and Kazienko P. On Measuring the Complexity of Networks: Kolmogorov Complexity versus Entropy. Complexity 2017;2017(3250301):1-12.
- Yılmaz N, Akilli M, Ozbek M, Zeren T, Akdeniz KG. Application of the nonlinear methods in pneumocardiogram signals. J Biol Phys 2020;46(2):209-222.
- Umberto L, Thomas DS, Giulia G. Entropy-Based Pandemics Forecasting. Front Phys 2020;8:274.
- Ghanbari A, Khordad R, Ghaderi-Zefrehei M. Mathematical prediction of the spreading rate of COVID-19 using entropy-based thermodynamic model. Indian J Phys 2021;95:2567–2573.
- Gibbs JW. Elementary Principles in Statistical Mechanics. New York: C. Scribner’s Sons,1902.
- Shannon CE. A Mathematical Theory of Communication. Bell Syst Tech J 1948;27(3):379–423.
- Jaynes ET. Information Theory and Statistical Mechanics. Phys Rev 1957;106(4):620-630.
- Penrose O. Foundations of Statistical Mechanics: A Deductive Treatment. Oxford: Pergamon, 1970.
- Gray RM. Entropy and Information Theory. Berlin: Springer, 2009.
- Beck C. Generalized information and entropy measures in physics. Contemp Phys 2009;50(4):495–510.
- Akıllı M, Yılmaz N and Akdeniz KG. Study of the q-Gaussian Distribution with the Scale Index and Calculating Entropy by Normalized Inner Scalogram. Phys Lett A 2019;383(11):1099-1104.
- Ritchie H, Mathiew E, Rodes-Guirao L et al. Coronavirus Pandemic (COVID-19) [online]. Available at: https://ourworldindata.org/coronavirus. Accessed September 2,2021.
- Gubrium N, Gubrium E. Narrative complexity in the time of COVID-19. Lancet 397(10291):2244-2245.
- Darby AC and Hiscox JA. Covid-19: variants and vaccination. BMJ 2021;372.
Details
| Primary Language | English |
|---|---|
| Subjects | Health Care Administration |
| Journal Section | Original Research |
| Authors | |
| Publication Date | August 5, 2022 |
| Submission Date | November 25, 2021 |
| Acceptance Date | March 13, 2022 |
| Published in Issue | Year 2022 Volume: 20 Issue: 2 |
Cite
TURKISH JOURNAL OF PUBLIC HEALTH - TURK J PUBLIC HEALTH. online-ISSN: 1304-1096
Copyright holder Turkish Journal of Public Health. This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. 