ESTIMATION OF DAILY CASES OF COVID-19 AND REPRODUCTION NUMBER IN USA, GERMANY, INDIA, RUSSIA, ITALY, SPAIN, FRANCE, UNITED KINGDOM, BRAZIL USING DISCRETE TIME GOMPERTZ MODEL AND ADAPTIVE KALMAN FILTER

Year 2021, Volume: 22 Issue: 3, 239 - 259, 29.09.2021

Levent Özbek , Hakan Demirtaş

https://doi.org/10.18038/estubtda.840307

Abstract

In this study, cumulative and daily cases are estimated online using discrete-time Gompertz model (DTGM) and Adaptive Kalman Filter (AKF) based on the total COVID-19 cases between February 29-July 28, 2020 in USA, Germany, India, Russia, Italy, Spain, France, United Kingdom, Brazil. Employing the data collected between February 29 and July 28, 2020, it is showed that the DTGM in conjunction with AKF provides a good analysis tool for modeling the daily cases made using the in terms of mean square error (MSE), mean absolute percentage error (MAPE), and R^2.

Keywords

COVID-19, Gompertz models, adaptive Kalman filter

ESTIMATION OF DAILY CASES OF COVID-19 AND REPRODUCTION NUMBER IN USA, GERMANY, INDIA, RUSSIA, ITALY, SPAIN, FRANCE, UNITED KINGDOM, BRAZIL USING DISCRETE TIME GOMPERTZ MODEL AND ADAPTIVE KALMAN FILTER

Abstract

References

• [1] Gorbalenya AE, Baker SC, Baric RS, et al. The Species Severe Acute Respiratory Syndrome-Related Coronavirus. Classifying 2019-Ncov and Naming It SARS–Cov-2. Nat Microbiol 2020;5.536–44.
• [2] Li Q, Guan X, Wu P, Wang X, Zhou L, Tong, Y, Feng Z. Early Transmission Dynamics in Wuhan, China, of Novel Coronavirus–Infected Pneumonia N Engl J Med 2020; 382:1199-1207.
• [3] World Health Organization. Novel coronavirus (2019-nCoV) situation reports.(2020); https.//www.who.int/emergencies/diseases/novel-coronavirus-2019/.
• [4] Jia L, Li K, Jiang Y, Guo X, Zhao, T. Prediction and analysis of coronavirus disease 2019. 2020; arXiv preprint arXiv.2003.05447.
• [5] Castorina, P, Iorio A, Lanteri D. Data analysis on coronavirus spreading by macroscopic growth laws.2020; arXiv preprint arXiv.20 03.0 0507.
• [6] Roosa K, Lee Y, Luo R, Kirpich A, Rothenberg R, Hyman JM, Yan P, Chowell G. Real-time forecasts of the COVID-19 epidemic in China from February 5th to February 24th. Infectious Disease Modelling 2020; 5, 256-263.
• [7] Roosa K, Lee Y, Luo R, Kirpich A, Rothenberg R, Hyman JM, Yan P, Chowell G. Short-term Forecasts of the COVID-19 Epidemic in Guangdong and Zhejiang, China. February 13–23. 2020; J. Clin. Med. 2020, 9, 596.
• [8] Munayco V, Tariq A, Rothenberg R, Gabriela G, Cabezas S, Reyes MF, Valle A, Mezarina LR, Cabezas C, Loayza M, Chowell G. Peru COVID-19 working Group Early transmission dynamics of COVID-19 in a southern hemisphere setting. Lima-Peru. February 29 the March 30th. 2020; Infectious Disease Modelling. 2020; 5, 338-345.
• [9] Rodriguez OT, Gutiérrez RAC, Javier ALH. Modeling and prediction of COVID-19 in Mexico applying mathematical and computational models. 2020; Chaos Solitons and Fractals 138, 109946.
• [10] Mazurek J, Nenickova Z. Predicting the number of total COVID-19 cases in the USA by a Gompertz curve. 2020; https.//www.researchgate.net/publication/340738553
• [11] Catal M, Alonso S, Lacalle EA, L´opez D, Cardona PJ, Prats C. Empiric model for short-time prediction of COVID-19 spreading. 2020; medRxiv https.//doi.org/10.1101/2020.05.13.20101329
• [12] Petropoulos F, Makridakis S. Forecasting the novel coronavirus COVID-19. PLOS ONE. 2020; https.//doi.org/10.1371/journal.pone.0231236 March 31.
• [13] Gompertz, B. On the nature of the function expressive of the law of human mortality, and on a new mode of determining the value of life contingencies. In a letter to Francis Baily, Esq. FRS &c. Philosophical transactions of the Royal Society of London. 1825;115:13–583.
• [14] Zwietering M, Jongenburger I, Rombouts F, Riet VK. Modeling of the bacterial growth curve. Appl Environ Microbiol 1990;56(6):1875–1881.
• [15] Gerlee P. The model muddle. in search of tumor growth laws. Cancer research 2013; 73(8):2407–2411.
• [16] Kathleen MC, Tjørve E. The use of Gompertz models in growth analyses, and new Gompertz-model approach. An addition to the Unified-Richards family. PLoS ONE 2017;12(6), e0178691.
• [17] Dennis B, Ponciano JM, Subhash R, Traper LM, Staples DF. Estimating Density Dependence, Process Noise and Observation Erros. Ecological Monographs 2006;76(3): 323–341.
• [18] Jazwinski, AH. Stochastic Processes and Filtering Theory. Academic Press, 1970.
• [19] Anderson, BDO, Moore JB. Optimal Filtering. Prentice Hall, 1979.
• [20] Chui, C.K, Chen G. Kalman Filtering with Real-time Applications. Springer Verlag, 1991.
• [21] Ljung, L, Söderström T. Theory and Practice of Recursive Identification. The MIT Press,1993.
• [22] Chen, G. Approximate Kalman Filtering. World Scientific, 1993.
• [23] Grewal S, Andrews AP. Kalman Filtering Theory and Practice. Prentice Hall, 1993.
• [24] Öztürk F, Özbek L. Mathematical Modelling and Simulation, Pigeon Yay, 2016 (in Turkish).
• [25] Özbek L. Kalman Filtresi, Akademisyen Yay. 2017 (in Turkish).
• [26] Kalman RE. A new Approach to linear Filtering and Prediction Problems”. Journal of Basic Engineering. 1960;82:35-45.
• [27] Cori A, Ferguson NM, Fraser C, Cauchemez S. A new framework and software to estimate time-varying reproduction numbers during epidemics. Am J Epidemiol 2013;178(9):1505-1512.
• [28] Özbek L, Aliev FA. Comments on Adaptive Fading Kalman Filter with an Application. Automatica 1998; 34(12): 1663-1664.
• [29] Efe M, Özbek L. Fading Kalman Filter for Manoeuvring Target Tracking. Journal of the Turkish Statistical Assocation 1999; 2(3):193-206.
• [30] Özbek L, Efe M. An Adaptive Extended Kalman Filter with Application to Compartment Models. Communications In Statistics-Simulation And Computation 2004; 33(1): 145-158.
• [31] Johns Hopkins University Center for Systems Science and Engineering, 2020. ttps.//github.com/CSSEGISandData/COVID-19.