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Unknown SIR parameters’ estimation of COVID-19 spread in Turkey by using RSS method

Year 2021, Volume: 11 Issue: 3, 956 - 963, 15.07.2021
https://doi.org/10.17714/gumusfenbil.757291

Abstract

Ending the global COVID-19 outbreak requires multiple country-wide strategies, such as social isolation, multiple tests, and monitoring people's interactions with each other. Many countries in the world have brought their own restrictions. Many parameters such as hospital capacities, social life and economy were taken into consideration while introducing the restrictions. Some countries, such as Italy, Brazil, and even the United States, have failed to predict the course of the outbreak and did not take more stringent measures, therefore; the outbreak has caused thousands of lives and is still happening. In this study, by considering the number of COVID-19 cases and the measures taken by the government, a model was developed to track the course of the epidemic for 91 days. For modeling, the SIR (Susceptible-Infected-Recovered) model, which is widely used in epidemiology was used. To estimate the parameters in the SIR model, RSS (Residual Sum of Squares) method was utilized. By taking into account the important time intervals, such as closure of the schools, country wide lockdowns and bending the restrictions, the model parameters were estimated for these intervals using the epidemic data given by the Ministry of Health. In addition, simulation results are provided to predict how the course of the epidemic would take place if precautions were not taken at the beginning of the outbreak or if the most recent measures were continued. This model offers authorities a preliminary assessment opportunity to manage the outbreak.

References

  • Alanazi, S.A., Kamruzzaman, M.M., Alruwaili, M., Alshammari, N., Alqahtani, S.A. and Karime, A. (2020). Measuring and preventing COVID-19 using the SIR model and machine learning. Smart Health Care Journal of Healthcare Engineering 8, 1-12. https://doi.org/10.1155/2020/8857346
  • Almeida R., Brito da Cruz A., Martins N. and Monteiro M. (2019). An epidemiological MSEIR model described by the Caputo fractional derivative. International Journal of Dynamics and Control. International Journal of Dynamics and Control, 7, 776-784. https://doi.org/10.1007/s40435-018-0492-1.
  • Brauer, F. and Castillo-Chavez, C. (2001). Mathematical models in population biology and epidemiology. New York: Springer.
  • Brauer, F. (2017). Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling, 2, 113–127.
  • Chowell, G. (2017). Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts. Infectious Disease Modelling, 2, 379–398.
  • Dandekar, R., and Barbastathis, G. (2020). Quantifying the effect of quarantine control in COVID-19 infectious spread using machine learning. medRxiv. 1-13. https://doi.org/10.1101/2020.04.03.20052084.
  • Eroglu, E., Bozkurt, E., Esenpinar, A.A. and Tek, S. (2020). Mathematical analysis of Covid-19 phenomenon. Journal of Engineering Technology and Applied Sciences, 5, 59-64. https://doi.org/10.30931/jetas.739270
  • Health Organization, Coronavirus disease (COVID-19) outbreak, https://www.who.int/emergencies/diseases/novel- coronavirus-2019.
  • Kermack, W. O. and McKendrick A G. A. (1927). Contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, (ss, 700–721)
  • Kermack, W. O. and McKendrick, A. G. (1932). Contributions to the mathematical theory of epidemics, II - the problem of endemicity. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 138, (5), 5–83.
  • Kraemer, M. U., Yang, C. H., Gutierrez, B., Wu, C. H., Klein, B., Pigott, D. M. and Brownstein, J. S. (2020). The effect of human mobility and control measures on the COVID-19 epidemic in China. Science, 368 (6490), 493-497.
  • Ndiaye B., Tendeng, L. and Seck, D. (2020). Analysis of the COVID-19 pandemic by SIR model and machine learning technics for forecasting. arXiv.org > q-bio > arXiv:2004.01574v1
  • Nesteruk, I. (2020). Estimations of the coronavirus epidemic dynamics in South Korea with the use of SIR model. https://doi.org/10.13140/RG.2.2.15489.40807
  • Pulla, P. (2020). COVID-19: India imposes lockdown for 21 days and cases rise. https://doi.org/10.1136/bmj.m1251. Ranjan, R. (2020). Predictions for COVID-19 outbreak in India using Epidemiological models. medRxiv. https://doi.org/10.1101/2020.04.02.20051466.
  • Türkiye Cumhuriyeti Sağlık Bakanlığı, Koronovirüs (COVID_19) salgını https://covid19bilgi.saglik.gov.tr/tr/haberler/turkiye-deki-gunluk-COVID-19-vaka-sayilari.html
  • Vyasarayani, C.P. and Chatterjee, A. (2020). Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity. Nonlinear Dynamics 101, 1653–1665. https://doi.org/10.1007/s11071-020-05785-2
  • WHO (2020). Naming the coronavirus disease (COVID-19) and the virus that causes it, https://www.who.int/emergencies/diseases/novel-coronavirus-2019/technical-guidance.
  • Wikipedia, Türkiye'de COVID-19 pandemisi, https://tr.wikipedia.org/wiki/T%C3%BCrkiye%27de_COVID-19_pandemisi_zaman_%C3%A7izelgesi
  • Wu, J. T., Leung, K., and Leung, G. M. (2020). Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. The Lancet, 395 (10225), 689–697.

Türkiye’deki COVID-19 yayılımının SIR temelli modellenmesinde RSS yöntemi ile parametre kestirimi

Year 2021, Volume: 11 Issue: 3, 956 - 963, 15.07.2021
https://doi.org/10.17714/gumusfenbil.757291

Abstract

Global COVID-19 salgınını sona erdirmek, sosyal izolasyon, çok sayıda test ve insanların birbirleriyle olan iletişimini izleme gibi ülke çapında geçerli birden çok stratejinin uygulanmasını gerektirir. Bu kapsamda, dünya üzerinde birçok ülke kendine özgü kısıtlamalar getirdi. Kısıtlamalar getirilirken hastane kapasiteleri, sosyal hayat ve ekonomi gibi birçok parametre dikkate alındı. İtalya, Brezilya ve hatta Amerika Birleşik Devletleri gibi bazı ülkeler, salgının seyrini kestiremeyip daha sıkı önlemler almayınca salgın binlerce can kaybına sebep oldu ve halen de olmaktadır. Bu çalışmada Türkiye’de görülen vaka sayılarıyla ve alınan tedbirler doğrultusunda salgının başlangıcından itibaren 91 gün boyunca nasıl bir seyir izlediğinin modellenmesi yapılmıştır. Modelleme yapılırken, epidemiyolojide yaygın olarak kullanılan SIR (Susceptable-Infected-Recovered, Korunmasız-Enfekte-Bulaşıcı Olmayan) modeli kullanılmıştır. Modellemede, parametre kestirimi için RSS (Residual Sum of Squares, Kalan Kareler) yönteminden faydalanılmıştır. Okulların tatil edilmesi, sokağa çıkma yasakları ve alınan tedbirlerin kısmen kaldırılması gibi önemli tarih aralıkları ayrı ayrı dikkate alınarak yapılan parametre kestirimleri ile T.C. Sağlık Bakanlığınca verilen salgın verilerine uygun bir modelleme yapılmıştır. Ayrıca, salgın başlangıcında önlem alınmasaydı ya da en son alınan tedbirler devam ettirilirse salgının seyrinin nasıl gerçekleşebileceğini öngören sonuçlar verilmiştir. Bu model, yetkililere salgını yönetmek için bir ön değerlendirme imkânı sunmaktadır.

References

  • Alanazi, S.A., Kamruzzaman, M.M., Alruwaili, M., Alshammari, N., Alqahtani, S.A. and Karime, A. (2020). Measuring and preventing COVID-19 using the SIR model and machine learning. Smart Health Care Journal of Healthcare Engineering 8, 1-12. https://doi.org/10.1155/2020/8857346
  • Almeida R., Brito da Cruz A., Martins N. and Monteiro M. (2019). An epidemiological MSEIR model described by the Caputo fractional derivative. International Journal of Dynamics and Control. International Journal of Dynamics and Control, 7, 776-784. https://doi.org/10.1007/s40435-018-0492-1.
  • Brauer, F. and Castillo-Chavez, C. (2001). Mathematical models in population biology and epidemiology. New York: Springer.
  • Brauer, F. (2017). Mathematical epidemiology: Past, present, and future. Infectious Disease Modelling, 2, 113–127.
  • Chowell, G. (2017). Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts. Infectious Disease Modelling, 2, 379–398.
  • Dandekar, R., and Barbastathis, G. (2020). Quantifying the effect of quarantine control in COVID-19 infectious spread using machine learning. medRxiv. 1-13. https://doi.org/10.1101/2020.04.03.20052084.
  • Eroglu, E., Bozkurt, E., Esenpinar, A.A. and Tek, S. (2020). Mathematical analysis of Covid-19 phenomenon. Journal of Engineering Technology and Applied Sciences, 5, 59-64. https://doi.org/10.30931/jetas.739270
  • Health Organization, Coronavirus disease (COVID-19) outbreak, https://www.who.int/emergencies/diseases/novel- coronavirus-2019.
  • Kermack, W. O. and McKendrick A G. A. (1927). Contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, (ss, 700–721)
  • Kermack, W. O. and McKendrick, A. G. (1932). Contributions to the mathematical theory of epidemics, II - the problem of endemicity. Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences. The Royal Society, 138, (5), 5–83.
  • Kraemer, M. U., Yang, C. H., Gutierrez, B., Wu, C. H., Klein, B., Pigott, D. M. and Brownstein, J. S. (2020). The effect of human mobility and control measures on the COVID-19 epidemic in China. Science, 368 (6490), 493-497.
  • Ndiaye B., Tendeng, L. and Seck, D. (2020). Analysis of the COVID-19 pandemic by SIR model and machine learning technics for forecasting. arXiv.org > q-bio > arXiv:2004.01574v1
  • Nesteruk, I. (2020). Estimations of the coronavirus epidemic dynamics in South Korea with the use of SIR model. https://doi.org/10.13140/RG.2.2.15489.40807
  • Pulla, P. (2020). COVID-19: India imposes lockdown for 21 days and cases rise. https://doi.org/10.1136/bmj.m1251. Ranjan, R. (2020). Predictions for COVID-19 outbreak in India using Epidemiological models. medRxiv. https://doi.org/10.1101/2020.04.02.20051466.
  • Türkiye Cumhuriyeti Sağlık Bakanlığı, Koronovirüs (COVID_19) salgını https://covid19bilgi.saglik.gov.tr/tr/haberler/turkiye-deki-gunluk-COVID-19-vaka-sayilari.html
  • Vyasarayani, C.P. and Chatterjee, A. (2020). Complete dimensional collapse in the continuum limit of a delayed SEIQR network model with separable distributed infectivity. Nonlinear Dynamics 101, 1653–1665. https://doi.org/10.1007/s11071-020-05785-2
  • WHO (2020). Naming the coronavirus disease (COVID-19) and the virus that causes it, https://www.who.int/emergencies/diseases/novel-coronavirus-2019/technical-guidance.
  • Wikipedia, Türkiye'de COVID-19 pandemisi, https://tr.wikipedia.org/wiki/T%C3%BCrkiye%27de_COVID-19_pandemisi_zaman_%C3%A7izelgesi
  • Wu, J. T., Leung, K., and Leung, G. M. (2020). Nowcasting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modelling study. The Lancet, 395 (10225), 689–697.
There are 19 citations in total.

Details

Primary Language Turkish
Subjects Engineering
Journal Section Articles
Authors

Nurbanu Güzey 0000-0002-6587-2489

Publication Date July 15, 2021
Submission Date June 24, 2020
Acceptance Date June 13, 2021
Published in Issue Year 2021 Volume: 11 Issue: 3

Cite

APA Güzey, N. (2021). Türkiye’deki COVID-19 yayılımının SIR temelli modellenmesinde RSS yöntemi ile parametre kestirimi. Gümüşhane Üniversitesi Fen Bilimleri Dergisi, 11(3), 956-963. https://doi.org/10.17714/gumusfenbil.757291