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Türkiye'de CoronaVac ile Kovid-19 Aşılama Başlangıcında Sars-Cov-2 Yayılımının Matematiksel Modellenmesi

Year 2023, , 1 - 14, 31.12.2023
https://doi.org/10.52693/jsas.1355520

Abstract

İlk olarak Çin'in Wuhan kentinde tespit edilen Sars-CoV-2 virüsü, tüm dünyayı etkileyen küresel bir krize dönüştü ve Mart 2020'de Dünya Sağlık Örgütü (DSÖ) tarafından pandemi ilan edildi. İnsanlığın karşı karşıya olduğu pandemilerle mücadelede en temel koruyucu önlem aşılamadır. Bu noktadan hareketle 13 Ocak - 11 Şubat 2021 tarihleri arasında Türkiye'deki günlük vaka, ölüm ve iyileşen hasta sayıları alınarak veriler toplanmıştır. Bu süre zarfında Türkiye'de Sinovac'ın CoronaVac aşısı ile Covid-19'a karşı aşılama başlatılmıştır. Gözlenen değerlerin matematiksel tahmin modelleri, polinom regresyon (3. dereceye kadar) ve doğrusal olmayan regresyon, yani eğri uydurma yöntemleri ve adi diferansiyel denklemler (ODE'ler) sistemi olan SIR (Susceptible-Infected-Removed) kullanılarak oluşturulmuş ve karşılaştırılmıştır. Bu tahmin modellerinin etkinlikleri test edilmiş, doğrulanmış ve en etkili matematiksel tahmin modelleri önerilmiştir. Kök ortalama kare hata (RMSE) ve ortalama mutlak yüzde hata (MAPE) değerleri, yöntemleri karşılaştırmak için performans ölçütleri olarak kullanılmaktadır. Önerilen tahmin modelleri aynı zamanda öngörü için de kullanılmıştır. Her gün meydana gelen yeni vaka sayısı, Euler yöntemi kullanılarak çözülen SIR yönteminin zamana bağlı denklemleri kullanılarak tahmin edilmiştir. SIR yönteminin diğer yöntemlere kıyasla gözlenen değerleri tahmin etmede oldukça başarılı olduğu, ancak QR yönteminin toplam ölüm sayısını tahmin etmede daha başarılı sonuçlar verdiği tespit edilmiştir.

References

  • [1] F. Zhou et al., “Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study,” The Lancet, vol. 395, no. 10229, pp. 1054–1062, Mar. 2020, doi: 10.1016/S0140-6736(20)30566-3.
  • [2] A. L. Phelan, R. Katz, and L. O. Gostin, “The Novel Coronavirus Originating in Wuhan, China: Challenges for Global Health Governance,” JAMA, vol. 323, no. 8, pp. 709–710, Feb. 2020, doi: 10.1001/jama.2020.1097.
  • [3] Coronaviridae Study Group of the International Committee on Taxonomy of Viruses et al., “The species Severe acute respiratory syndrome-related coronavirus: classifying 2019-nCoV and naming it SARS-CoV-2,” Nat. Microbiol., vol. 5, no. 4, pp. 536–544, Mar. 2020, doi: 10.1038/s41564-020-0695-z.
  • [4] J. W. M. Chan et al., “Short term outcome and risk factors for adverse clinical outcomes in adults with severe acute respiratory syndrome (SARS),” Thorax, vol. 58, no. 8, pp. 686–689, Aug. 2003, doi: 10.1136/thorax.58.8.686.
  • [5] M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals. Princeton University Press, 2011. doi: 10.1515/9781400841035.
  • [6] O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. John Wiley & Sons, 2000.
  • [7] F. Arroyo-Marioli, F. Bullano, S. Kucinskas, and C. Rondón-Moreno, “Tracking R of COVID-19: A new real-time estimation using the Kalman filter,” PLOS ONE, vol. 16, no. 1, p. e0244474, Jan. 2021, doi: 10.1371/journal.pone.0244474.
  • [8] A.-J. Valleron, “Roles of mathematical modelling in epidemiology,” COMPTES RENDUS-Acad. Sci. PARIS Ser. 3, vol. 323, no. 5, pp. 429–434, 2000.
  • [9] F. Brauer, “Lecture Notes in Mathematical Epidemiology”.
  • [10] M. Martcheva, An Introduction to Mathematical Epidemiology, vol. 61. in Texts in Applied Mathematics, vol. 61. Boston, MA: Springer US, 2015. doi: 10.1007/978-1-4899-7612-3 . [11] N. M. Ferguson, “Mathematical prediction in infection,” Medicine (Baltimore), vol. 37, no. 10, pp. 507–509, Oct. 2009, doi: 10.1016/j.mpmed.2009.07.004.
  • [12] M. Abotaleb et al., “Modeling Covid-19 Infection Cases and Vaccine in 5 Countries Highly Vaccinations,” Turk. J. Math. Comput. Sci., vol. 13, no. 2, pp. 403–417, Dec. 2021, doi: 10.47000/tjmcs.905508.
  • [13] Z. Liao, P. Lan, Z. Liao, Y. Zhang, and S. Liu, “TW-SIR: time-window based SIR for COVID-19 forecasts,” Sci. Rep., vol. 10, no. 1, Art. no. 1, Dec. 2020, doi: 10.1038/s41598-020-80007-8.
  • [14] İ. Demi̇r and M. Ki̇ri̇sci̇, “Forecasting COVID-19 Disease Cases Using the SARIMA-NNAR Hybrid Model,” Univers. J. Math. Appl., vol. 5, no. 1, Art. no. 1, Mar. 2022, doi: 10.32323/ujma.1010490.
  • [15] A. Adiga, D. Dubhashi, B. Lewis, M. Marathe, S. Venkatramanan, and A. Vullikanti, “Mathematical Models for COVID-19 Pandemic: A Comparative Analysis,” J. Indian Inst. Sci., vol. 100, no. 4, pp. 793–807, Oct. 2020, doi: 10.1007/s41745-020-00200-6.
  • [16] E. Eroglu, A. A. Esenpinar, E. Bozkurt, and S. Tek, “Mathematical Modeling of Covid-19 Phenomenon; The Cases: Germany, Israel and Canada,” Fresenius Environ. Bull., vol. 29, no. 10, pp. 9063–9074.
  • [17] B. M. Ndiaye, L. Tendeng, and D. Seck, “Analysis of the COVID-19 pandemic by SIR model and machine learning technics for forecasting.” arXiv, Apr. 03, 2020. doi: 10.48550/arXiv.2004.01574.
  • [18] A. A. Toda, “Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact.” arXiv, Mar. 26, 2020. doi: 10.48550/arXiv.2003.11221.
  • [19] H. (Howie) Weiss, “The SIR model and the Foundations of Public Health,” Mater. Matemàtics, pp. 1–17, 2013.
  • [20] B. Barrett, “Regression Analysis: Concepts and Applications,” Technometrics, vol. 37, no. 2, pp. 229–229, 1995, doi: 10.1080/00401706.1995.10484308.
  • [21] “Genel Koronavirüs Tablosu.” Accessed: Sep. 05, 2023. [Online]. Available: https://covid19.saglik.gov.tr/TR-66935/genel-koronavirus-tablosu.html
  • [22] H. L. Seal, “Studies in the History of Probability and Statistics. XV: The Historical Development of the Gauss Linear Model,” Biometrika, vol. 54, no. 1/2, pp. 1–24, 1967, doi: 10.2307/2333849.
  • [23] J. D. Gergonne, “The application of the method of least squares to the interpolation of sequences,” Hist. Math., vol. 1, no. 4, pp. 439–447, Nov. 1974, doi: 10.1016/0315-0860(74)90034-2.
  • [24] S. Bakanlığı, “Temaslı takibi, salgın yönetimi, evde hasta izlemi ve filyasyon,” Bilimsel Danışma Kurulu Ank. Halk Sağlığı Genel Müdürlüğü, 2020.

Mathematical Modeling of the Spread of Sars-Cov-2 at the Onset of Vaccination Against Covid-19 with CoronaVac in Türkiye

Year 2023, , 1 - 14, 31.12.2023
https://doi.org/10.52693/jsas.1355520

Abstract

The Sars-CoV-2 virus, first detected in Wuhan, China, became a global crisis that affected the entire world and was declared a pandemic by the World Health Organization (WHO) in March 2020. The most basic protective measure in the fight against pandemics facing humanity is vaccination. From this point of view, data is collected between January 13 and February 11, 2021 by taking the number of daily cases, deaths and recovered patients in Türkiye. During this period, vaccination against Covid-19 with Sinovac's CoronaVac vaccine is started in Türkiye. Mathematical predictive models of the observed values are constructed and compared using polynomial regression (up to the 3rd degree) and nonlinear regression, i.e., curve fitting methods, and SIR (Susceptible-Infected-Removed), which is a system of ordinary differential equations (ODEs). The efficiencies of these prediction models are tested, validated, and the most effective mathematical prediction models are proposed. The values of root mean square error (RMSE) and mean absolute percentage error (MAPE) are used as performance measures to compare the methods. The proposed prediction models are also used for forecasting. The number of new cases occurring each day is predicted using the time-dependent equations of the SIR method, which are solved using the Euler method. It is found that the SIR method is quite successful in predicting the observed values compared to the other methods, but the QR method are given more successful results in predicting the total number of deaths

References

  • [1] F. Zhou et al., “Clinical course and risk factors for mortality of adult inpatients with COVID-19 in Wuhan, China: a retrospective cohort study,” The Lancet, vol. 395, no. 10229, pp. 1054–1062, Mar. 2020, doi: 10.1016/S0140-6736(20)30566-3.
  • [2] A. L. Phelan, R. Katz, and L. O. Gostin, “The Novel Coronavirus Originating in Wuhan, China: Challenges for Global Health Governance,” JAMA, vol. 323, no. 8, pp. 709–710, Feb. 2020, doi: 10.1001/jama.2020.1097.
  • [3] Coronaviridae Study Group of the International Committee on Taxonomy of Viruses et al., “The species Severe acute respiratory syndrome-related coronavirus: classifying 2019-nCoV and naming it SARS-CoV-2,” Nat. Microbiol., vol. 5, no. 4, pp. 536–544, Mar. 2020, doi: 10.1038/s41564-020-0695-z.
  • [4] J. W. M. Chan et al., “Short term outcome and risk factors for adverse clinical outcomes in adults with severe acute respiratory syndrome (SARS),” Thorax, vol. 58, no. 8, pp. 686–689, Aug. 2003, doi: 10.1136/thorax.58.8.686.
  • [5] M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals. Princeton University Press, 2011. doi: 10.1515/9781400841035.
  • [6] O. Diekmann and J. A. P. Heesterbeek, Mathematical Epidemiology of Infectious Diseases: Model Building, Analysis and Interpretation. John Wiley & Sons, 2000.
  • [7] F. Arroyo-Marioli, F. Bullano, S. Kucinskas, and C. Rondón-Moreno, “Tracking R of COVID-19: A new real-time estimation using the Kalman filter,” PLOS ONE, vol. 16, no. 1, p. e0244474, Jan. 2021, doi: 10.1371/journal.pone.0244474.
  • [8] A.-J. Valleron, “Roles of mathematical modelling in epidemiology,” COMPTES RENDUS-Acad. Sci. PARIS Ser. 3, vol. 323, no. 5, pp. 429–434, 2000.
  • [9] F. Brauer, “Lecture Notes in Mathematical Epidemiology”.
  • [10] M. Martcheva, An Introduction to Mathematical Epidemiology, vol. 61. in Texts in Applied Mathematics, vol. 61. Boston, MA: Springer US, 2015. doi: 10.1007/978-1-4899-7612-3 . [11] N. M. Ferguson, “Mathematical prediction in infection,” Medicine (Baltimore), vol. 37, no. 10, pp. 507–509, Oct. 2009, doi: 10.1016/j.mpmed.2009.07.004.
  • [12] M. Abotaleb et al., “Modeling Covid-19 Infection Cases and Vaccine in 5 Countries Highly Vaccinations,” Turk. J. Math. Comput. Sci., vol. 13, no. 2, pp. 403–417, Dec. 2021, doi: 10.47000/tjmcs.905508.
  • [13] Z. Liao, P. Lan, Z. Liao, Y. Zhang, and S. Liu, “TW-SIR: time-window based SIR for COVID-19 forecasts,” Sci. Rep., vol. 10, no. 1, Art. no. 1, Dec. 2020, doi: 10.1038/s41598-020-80007-8.
  • [14] İ. Demi̇r and M. Ki̇ri̇sci̇, “Forecasting COVID-19 Disease Cases Using the SARIMA-NNAR Hybrid Model,” Univers. J. Math. Appl., vol. 5, no. 1, Art. no. 1, Mar. 2022, doi: 10.32323/ujma.1010490.
  • [15] A. Adiga, D. Dubhashi, B. Lewis, M. Marathe, S. Venkatramanan, and A. Vullikanti, “Mathematical Models for COVID-19 Pandemic: A Comparative Analysis,” J. Indian Inst. Sci., vol. 100, no. 4, pp. 793–807, Oct. 2020, doi: 10.1007/s41745-020-00200-6.
  • [16] E. Eroglu, A. A. Esenpinar, E. Bozkurt, and S. Tek, “Mathematical Modeling of Covid-19 Phenomenon; The Cases: Germany, Israel and Canada,” Fresenius Environ. Bull., vol. 29, no. 10, pp. 9063–9074.
  • [17] B. M. Ndiaye, L. Tendeng, and D. Seck, “Analysis of the COVID-19 pandemic by SIR model and machine learning technics for forecasting.” arXiv, Apr. 03, 2020. doi: 10.48550/arXiv.2004.01574.
  • [18] A. A. Toda, “Susceptible-Infected-Recovered (SIR) Dynamics of COVID-19 and Economic Impact.” arXiv, Mar. 26, 2020. doi: 10.48550/arXiv.2003.11221.
  • [19] H. (Howie) Weiss, “The SIR model and the Foundations of Public Health,” Mater. Matemàtics, pp. 1–17, 2013.
  • [20] B. Barrett, “Regression Analysis: Concepts and Applications,” Technometrics, vol. 37, no. 2, pp. 229–229, 1995, doi: 10.1080/00401706.1995.10484308.
  • [21] “Genel Koronavirüs Tablosu.” Accessed: Sep. 05, 2023. [Online]. Available: https://covid19.saglik.gov.tr/TR-66935/genel-koronavirus-tablosu.html
  • [22] H. L. Seal, “Studies in the History of Probability and Statistics. XV: The Historical Development of the Gauss Linear Model,” Biometrika, vol. 54, no. 1/2, pp. 1–24, 1967, doi: 10.2307/2333849.
  • [23] J. D. Gergonne, “The application of the method of least squares to the interpolation of sequences,” Hist. Math., vol. 1, no. 4, pp. 439–447, Nov. 1974, doi: 10.1016/0315-0860(74)90034-2.
  • [24] S. Bakanlığı, “Temaslı takibi, salgın yönetimi, evde hasta izlemi ve filyasyon,” Bilimsel Danışma Kurulu Ank. Halk Sağlığı Genel Müdürlüğü, 2020.
There are 23 citations in total.

Details

Primary Language English
Subjects Software Engineering (Other)
Journal Section Research Articles
Authors

Ersin Şener 0000-0002-5934-3652

Ümmü Şahin Şener 0000-0001-9055-8734

Publication Date December 31, 2023
Published in Issue Year 2023

Cite

IEEE E. Şener and Ü. Şahin Şener, “Mathematical Modeling of the Spread of Sars-Cov-2 at the Onset of Vaccination Against Covid-19 with CoronaVac in Türkiye”, JSAS, no. 8, pp. 1–14, December 2023, doi: 10.52693/jsas.1355520.