Araştırma Makalesi
BibTex RIS Kaynak Göster

LOJİSTİK BÜYÜME VE ÜSTEL BÜYÜME MODELLERİ İLE TÜRKİYE’DE COVID-19 MODELLEMESİ

Yıl 2020, Cilt: 2 Sayı: 1, 1 - 18, 30.06.2020

Öz

Lojistik Büyüme ve Üstel Büyüme modelleri çeşitli durumlarda kullanılabilen matematiksel birer fonksiyondur. Üstel Büyüme modelleri, durdurulamaz bir enfeksiyon büyümesini ifade ederek salgınların başlangıç dönemleri için bu büyümeye yeterli bir yaklaşım sağlayabilen bir yöntem iken Lojistik Büyüme modelleri, başlangıç döneminde büyümenin arttığı daha sonra maksimuma yaklaştıkça azalan büyümenin modellenmesinde karşımıza çıkan bir yöntemdir. Enfeksiyon salgınlarının büyümesinde, bu maksimum sınır dünyadaki toplam insan sayısı olacaktır, çünkü herkes hasta olduğunda büyüme mutlaka azalacaktır. Bu sebeple, son zamanlarda büyük bir hızla tüm dünyayı etkileyen COVID-19 salgın verilerinin modellenmesinde de bu yöntemler sıklıkla kullanılmaktadır. Bu çalışmada amaç, Türkiye’de 11 Mart 2020 – 19 Mayıs 2020 tarihleri arasında ortaya çıkan ve onaylanmış COVID-19 vakalarının toplam sayılarına ilişkin büyümeyi tanımlayan bir matematiksel model oluşturmaktır. Bu bağlamda, belirtilen tarihlerde Türkiye’de ortaya çıkan COVID-19 toplam vaka sayılarını kullanarak Lojistik Büyüme, Lojistik ve Üstel Büyüme modelleri oluşturulmuştur. Ayrıca, oluşturulan bu modeller ile vaka sayılarının seyrini öngörme yeteneğini de gözlemlemek hedeflenmiştir. Modelleme çalışmasına ilişkin çözümlemeler Python programlama dilinde yer alan bazı fonksiyonlar ile gerçekleştirilerek çıkan sonuçlar yorumlanmıştır.

Kaynakça

  • Batista, M. (2020a), Estimation of the final size of the coronavirus epidemic by the SIR model, [Preprint] MedRxiv, E-pub: 21.03.2020, https://doi.org/10.1101/2020.02.16.20023606.
  • Batista, M. (2020b), Estimation of the final size of the second phase of the coronavirus epidemic by the logistic model [Preprint] MedRxiv, E-pub: 17.03.2020, https://doi.org/10.1101/2020.03.11.20024901.
  • Budak, F. ve Korkmaz, Ş. (2020), COVID-19 pandemi sürecine yönelik genel bir değerlendirme: Türkiye örneği, Sosyal Araştırmalar ve Yönetim Dergisi, 1, 62–79.
  • Chen, X. ve Yu, B. (2020), First two months of the 2019 coronavirus disease (COVID-19) epidemic in China: Real-time surveillance and evaluation with a second derivative model, Global Health Research and Policy, 5(1).
  • Clark, A. J., Lake, L. W. ve Patzek, T. W. (2011), Production forecasting with logistic growth models, SPE Annual Technical Conference and Exhibition, 1, 184–194.
  • Dattoli, G., Palma, D., Licciardi, S. ve Sabia, E. (2020), A note on the evolution of Covid-19 in Italy.
  • Grasselli, G., Pesenti, A. ve Cecconi, M. (2020), Critical care utilization for the COVID-19 outbreak in Lombardy, Italy, Journal of the American Medical Association, 323(16), 1545–1546.
  • Güzelkokar, G. (2020), COVID-19 in Turkey | Kaggle, Retrieved: 19.05.2020, https://www.kaggle.com/gkhan496/covid19-in-turkey.
  • http-1: https://www.kaggle.com, Erişim Tarihi: 02.06.2020.
  • Kirichu, S. K. (2020), Short-term projection of COVID 19 cases in Kenya using an exponential model [Preprint], Research Square, https://doi.org/10.21203/RS.3.RS-21900/V1.
  • Korstanje, J. (2020), Modeling logistic growth, https://towardsdatascience.com/modeling-logistic-growth-1367dc971de2.
  • Kriston L. Projection of cumulative coronavirus disease 2019 (COVID-19) case growth with a hierarchical logistic model [Preprint], Bull World Health Organ, E-pub: 07.04.2020, http://dx.doi.org/10.2471/BLT.20.257386.
  • Malato, G. (2020), Covid-19 infection in Italy Mathematical models and predictions, https://towardsdatascience.com/covid-19-infection-in-italy-mathematical-models-and-predictions-7784b4d7dd8d.
  • Oliveiros, B., Caramelo, L., Ferreira, N. C. ve Caramelo, F. (2020), Role of temperature and humidity in the modulation of the doubling time of COVID-19 cases [Preprint], MedRxiv, E-pub: 8.03.2020, https://doi.org/10.1101/2020.03.05.20031872.
  • Önder, H. (2020), Short-term forecasts of the COVID-19 epidemic in Turkey: March 16–28, 2020, Black Sea Journal of Health Science, 3(2), 27–30.
  • Roosa, K., Lee, Y., Luo, R., Kirpich, A., Rothenberg, R., Hyman, J. M., Yan, P., ve Chowell, G. (2020), Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020, Infectious Disease Modelling, 5, 256–263.
  • Shekhar, H. (2020), Prediction of spreads of COVID-19 in India from current trend. [Preprint]. MedRxiv, E-pub: 06.05.2020, https://doi.org/10.1101/2020.05.01.20087460.
  • Shen, C. Y. (2020), A logistic growth model for COVID-19 proliferation: Experiences from China and international implications in infectious diseases, International Journal of Infectious Diseases, https://doi.org/10.1016/j.ijid.2020.04.085.
  • Tsoularis, A. ve Wallace, J. (2002), Analysis of logistic growth models, Mathematical Biosciences, 179(1), 21–55.
  • Tuite, A. R. ve Fisman, D. N. (2020), Reporting, epidemic growth, and reproduction numbers for the 2019 novel coronavirus (2019-nCoV) epidemic, Annals of Internal Medicine, 172(8), 567–568.
  • Viboud, C., Simonsen, L. ve Chowell, G. (2016), A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks, Epidemics, 15, 27–37.
  • Vikipedi: Özgür Ansiklopedi (2020), Malthusçu büyüme örneği, Erişim Tarihi: 02.06.2020, https://tr.wikipedia.org/wiki/Malthusçu_Büyüme_Örneği.
  • Wu, K., Darcet, D., Wang, Q. ve Sornette, D. (2020), Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world [Preprint], MedRxiv, E-pub: 16.03.2020, https://doi.org/10.1101/2020.03.11.20034363.

MODELLING COVID-19 IN TURKEY WITH LOGISTIC GROWTH MODEL AND EXPONENTIAL GROWTH MODEL

Yıl 2020, Cilt: 2 Sayı: 1, 1 - 18, 30.06.2020

Öz

Exponential Growth Model is a method that can provide an adequate approach to this growth for the beginning periods of outbreaks by expressing an unstoppable infection growth, while Logistics Growth Model is a method that appears in the modeling of the growth that decreases as the growth increases in the initial period and then approaches the maximum. In the growth of infectious outbreaks, this maximum limit will be the total number of people in the world, because growth will certainly decrease when everyone is ill. For this reason, it is also frequently used in the modeling of COVID-19 data, which has recently affected the whole world with great speed. The purpose of this study is to create a statistical model that describes the growth in total number of COVID-19 confirmed cases which occurred the dates between March 11 and May 19, 2020 in Turkey. In this context, Logistic Growth and Exponential Growth models were created to analyze the total number of COVID-19 confirmed cases between the dates mentioned above. In addition to these models, another model called as Logistic Model, which is similar to the Logistics Growth Model and is used frequently in modeling population growth, is also used. With these models, it is also aimed to observe the ability to predict the course of the number of cases. Analyzes related to the modeling study were carried out using some functions in the Python programming language and the results were interpreted.

Kaynakça

  • Batista, M. (2020a), Estimation of the final size of the coronavirus epidemic by the SIR model, [Preprint] MedRxiv, E-pub: 21.03.2020, https://doi.org/10.1101/2020.02.16.20023606.
  • Batista, M. (2020b), Estimation of the final size of the second phase of the coronavirus epidemic by the logistic model [Preprint] MedRxiv, E-pub: 17.03.2020, https://doi.org/10.1101/2020.03.11.20024901.
  • Budak, F. ve Korkmaz, Ş. (2020), COVID-19 pandemi sürecine yönelik genel bir değerlendirme: Türkiye örneği, Sosyal Araştırmalar ve Yönetim Dergisi, 1, 62–79.
  • Chen, X. ve Yu, B. (2020), First two months of the 2019 coronavirus disease (COVID-19) epidemic in China: Real-time surveillance and evaluation with a second derivative model, Global Health Research and Policy, 5(1).
  • Clark, A. J., Lake, L. W. ve Patzek, T. W. (2011), Production forecasting with logistic growth models, SPE Annual Technical Conference and Exhibition, 1, 184–194.
  • Dattoli, G., Palma, D., Licciardi, S. ve Sabia, E. (2020), A note on the evolution of Covid-19 in Italy.
  • Grasselli, G., Pesenti, A. ve Cecconi, M. (2020), Critical care utilization for the COVID-19 outbreak in Lombardy, Italy, Journal of the American Medical Association, 323(16), 1545–1546.
  • Güzelkokar, G. (2020), COVID-19 in Turkey | Kaggle, Retrieved: 19.05.2020, https://www.kaggle.com/gkhan496/covid19-in-turkey.
  • http-1: https://www.kaggle.com, Erişim Tarihi: 02.06.2020.
  • Kirichu, S. K. (2020), Short-term projection of COVID 19 cases in Kenya using an exponential model [Preprint], Research Square, https://doi.org/10.21203/RS.3.RS-21900/V1.
  • Korstanje, J. (2020), Modeling logistic growth, https://towardsdatascience.com/modeling-logistic-growth-1367dc971de2.
  • Kriston L. Projection of cumulative coronavirus disease 2019 (COVID-19) case growth with a hierarchical logistic model [Preprint], Bull World Health Organ, E-pub: 07.04.2020, http://dx.doi.org/10.2471/BLT.20.257386.
  • Malato, G. (2020), Covid-19 infection in Italy Mathematical models and predictions, https://towardsdatascience.com/covid-19-infection-in-italy-mathematical-models-and-predictions-7784b4d7dd8d.
  • Oliveiros, B., Caramelo, L., Ferreira, N. C. ve Caramelo, F. (2020), Role of temperature and humidity in the modulation of the doubling time of COVID-19 cases [Preprint], MedRxiv, E-pub: 8.03.2020, https://doi.org/10.1101/2020.03.05.20031872.
  • Önder, H. (2020), Short-term forecasts of the COVID-19 epidemic in Turkey: March 16–28, 2020, Black Sea Journal of Health Science, 3(2), 27–30.
  • Roosa, K., Lee, Y., Luo, R., Kirpich, A., Rothenberg, R., Hyman, J. M., Yan, P., ve Chowell, G. (2020), Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th, 2020, Infectious Disease Modelling, 5, 256–263.
  • Shekhar, H. (2020), Prediction of spreads of COVID-19 in India from current trend. [Preprint]. MedRxiv, E-pub: 06.05.2020, https://doi.org/10.1101/2020.05.01.20087460.
  • Shen, C. Y. (2020), A logistic growth model for COVID-19 proliferation: Experiences from China and international implications in infectious diseases, International Journal of Infectious Diseases, https://doi.org/10.1016/j.ijid.2020.04.085.
  • Tsoularis, A. ve Wallace, J. (2002), Analysis of logistic growth models, Mathematical Biosciences, 179(1), 21–55.
  • Tuite, A. R. ve Fisman, D. N. (2020), Reporting, epidemic growth, and reproduction numbers for the 2019 novel coronavirus (2019-nCoV) epidemic, Annals of Internal Medicine, 172(8), 567–568.
  • Viboud, C., Simonsen, L. ve Chowell, G. (2016), A generalized-growth model to characterize the early ascending phase of infectious disease outbreaks, Epidemics, 15, 27–37.
  • Vikipedi: Özgür Ansiklopedi (2020), Malthusçu büyüme örneği, Erişim Tarihi: 02.06.2020, https://tr.wikipedia.org/wiki/Malthusçu_Büyüme_Örneği.
  • Wu, K., Darcet, D., Wang, Q. ve Sornette, D. (2020), Generalized logistic growth modeling of the COVID-19 outbreak in 29 provinces in China and in the rest of the world [Preprint], MedRxiv, E-pub: 16.03.2020, https://doi.org/10.1101/2020.03.11.20034363.
Toplam 23 adet kaynakça vardır.

Ayrıntılar

Birincil Dil Türkçe
Konular İstatistik
Bölüm Makaleler
Yazarlar

Şükriye Nur Şencan Bu kişi benim 0000-0003-2047-4265

Büşra Şencan Bu kişi benim 0000-0003-2717-4898

Müge Borazan Çelikbıçak 0000-0002-5796-9192

Duhan Arslan Bu kişi benim 0000-0002-4485-1777

Elif Su Özkan Bu kişi benim 0000-0001-9137-6318

Asu Şerife Gökçen Bu kişi benim 0000-0002-0101-459X

Ramazan Barış Çiftçi 0000-0002-7489-1956

İlayda Arıkan Bu kişi benim 0000-0001-6083-1752

Burak Uğur Bu kişi benim 0000-0001-8719-866X

Hanife Şahin 0000-0002-0924-5704

Ahmet Emircan Coşkun Bu kişi benim 0000-0002-3850-5499

Hande Konşuk Ünlü 0000-0003-3572-0254

Serpil Aktaş 0000-0003-3364-6388

Yayımlanma Tarihi 30 Haziran 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 2 Sayı: 1

Kaynak Göster

APA Şencan, Ş. N., Şencan, B., Borazan Çelikbıçak, M., Arslan, D., vd. (2020). LOJİSTİK BÜYÜME VE ÜSTEL BÜYÜME MODELLERİ İLE TÜRKİYE’DE COVID-19 MODELLEMESİ. Nicel Bilimler Dergisi, 2(1), 1-18.