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

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.

Anahtar Kelimeler:

COVID-19, RSS, SIR yayılım modeli

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

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.

Keywords:

COVID-19, RSS, SIR spread model,

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