Turkiye Klinikleri Journal of Biostatistics

.: ORIGINAL RESEARCH
A Study on the Estimation of COVID-19 Daily Cases and Reproduction Number Using Adaptive Kalman Filter for USA, Brazil, Germany, India, Russia, Italy, Spain, United Kingdom, France, Turkey
ABD, Brezilya, Almanya, Hindistan, Rusya, İtalya, İspanya, Birleşik Krallık, Fransa, Türkiye İçin Uyarlanabilir Kalman Filtresi Kullanarak COVID-19 Günlük Vakaları ve Üreme Sayısı Tahmini Üzerine Bir Çalışma
Levent ÖZBEKa, Hakan DEMİRTAŞb
aDepartment of Statistics, Ankara University Faculty of Science, Ankara, TURKEY
bDivision of Epidemiology and Biostatistics, University of Illinois at Chicago, Chicago, USA
Turkiye Klinikleri J Biostat. 2021;13(1):91-102
doi: 10.5336/biostatic.2020-80186
Article Language: EN
Full Text
ABSTRACT
 Objective: In the literature, non-linear mathematical growth models are often used to estimate the number of coronavirus disease-2019 (COVID-19) cases. Specific algorithms such as mathematical optimization technique need to be employed for parameter estimation. In this work, a novel method to estimate COVID-19 daily cases and reproduction number is proposed for COVID-19. Material and Methods: In this study, the daily number of COVID19 cases between January 01 and November 16, 2020 has been estimated online via AR(1) (autoregressive time-series model of order 1) and the adaptive Kalman filter (AKF). After calculating the estimate for daily cases, the reproduction number estimate was obtained. Results: It is quite a simple method to model the daily case number by time series with the time-varying parameter AR(1) stochastic process and estimated the time-varying parameter with online AKF. The method is online. Only the data points on the last day are sufficient. Conclusion: The COVID-19 data have been modeled in state space, and the AKF has been employed to estimate the number of daily cases. The estimation results were obtained for the number of daily cases using the AR(1) model. Since the estimation using the AR(1) stochastic process does not require any other modeling assumption, it is a simple approach to model the daily case number time series with the time-varying parameter AR(1) stochastic process and estimated the time-varying parameter with online AKF. We suggest that the simplest method for the reproduction number estimation will be obtained by modeling the daily case via an AR(1) model.

Keywords: COVID-19; state-space modelling; AR(1); adaptive Kalman filter; the reproduction number estimation
ÖZET
 Amaç: Literatürde, doğrusal olmayan matematiksel büyüme modelleri, koronavirüs hastalığı-2019 [coronavirus disease-2019 (COVID-19)] vakalarının sayısını tahmin etmek için sıklıkla kullanılmaktadır. Parametre tahmini için matematiksel optimizasyon tekniği gibi özel algoritmaların kullanılması gerekir. Bu çalışmada, COVID-19 için günlük COVID-19 vakalarını ve çoğalma sayısını tahmin etmek için yeni bir yöntem önerilmiştir. Gereç ve Yöntemler: Bu çalışmada, 01 Ocak ve 16 Kasım 2020 tarihleri arasında günlük COVID-19 vakalarına dayalı olarak AR(1) (1 gecikmeli oto regresif zaman serisi modeli) ve uyarlanabilir Kalman filtresi (UKF) aracılığıyla günlük vaka tahmini çevrim içi olarak yapılmıştır. Günlük vakalar için tahmin, çoğalma sayısı tahmini elde edilmiştir. Bulgular: Günlük vaka sayısı zaman serilerini zamanla değişen AR(1) stokastik süreç ile modellemek ve çevrimiçi UKF ile zamanla değişen parametreyi tahmin etmek oldukça basit bir yöntemdir. Yöntem çevrim içidir. Yalnızca son gündeki veri noktaları yeterlidir. Sonuç: COVID-19 verileri durum uzayında modellenmiştir ve günlük vaka sayısını tahmin etmek için UKF kullanılmıştır. AR(1) modeli kullanılarak günlük vaka sayısı için elde edilen tahmin sonuçları. AR(1) stokastik sürecini kullanan tahmin, başka herhangi bir modelleme varsayımı gerektirmediğinden, basit bir yaklaşımdır. Günlük vaka sayısı zaman serilerini zamanla değişen AR(1) stokastik süreci ile modellemek oldukça basit bir yöntemdir ve zamanla değişen parametreyi çevrim içi UKF ile tahmin edilmiştir. Çoğalma sayısı tahmini için en basit yöntemin, günlük vakayı bir AR(1) modeli aracılığıyla modelleyerek elde edileceğini öneriyoruz.

Anahtar Kelimeler: COVID-19; durum uzayı modellemesi; AR(1); uyarlamalı Kalman filtresi; çoğalma sayısı tahmini
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