JDS Journal of Data Science 1683-8602 1680-743X 1680-743X School of Statistics, Renmin University of China JDS991 10.6339/21-JDS991 Data Science in Action Time Series Regression Models for COVID-19 Deaths AndradeMarinho G.marinho@icmc.usp.br1∗ AchcarJorge A.2 ConceiçãoKatiane S.1 RavishankerNalini3 Department of Applied Mathematics and Statistics, ICMC, University of São Paulo, São Carlos/SP, Brazil Faculty of Medicine of Ribeirão Preto, University of São Paulo, Ribeirão Preto/SP, Brazil Department of Statistics, University of Connecticut, Storrs, CT, USA Corresponding author. Email: marinho@icmc.usp.br. 2021752021192269292 Supplementary Material

Supplementary material online include: rational functions and nonlinear rational polynomial model; tables with fitted model parameters and residual analysis; a brief Report for each of the countries that we considered; data and R code needed to reproduce the results.

 182020 1112020 2021 The Author(s). Published by the School of Statistics and the Center for Applied Statistics, Renmin University of China.2021 Open access article under the CC BY license.

This article develops nonlinear functional forms for modeling count time series of daily deaths due to the COVID-19 virus. Our models explain the mean levels of the time series while accounting for the time-varying variances. A Bayesian approach using Markov chain Monte Carlo (MCMC) is adopted for analysis, inference and forecasting of the time series under the proposed models. Applications are shown for time series of death counts from several countries affected by the pandemic.

 Bayesian approach nonlinear model pandemic cycle References Andersen KG, Rambaut A, Lipkin WI, Holmes EC, Garry RF (2020). The proximal origin of SARS-CoV-2. Nature Medicine, 26(4): 450–452. Bates DM, Watts DG (1988). Nonlinear Regression Analysis and Its Applications. Wiley, New York. Chan JFW, Yuan S, Kok KH, To KKW, Chu H, Yang J, et al. (2020). A familial cluster of pneumonia associated with the 2019 novel coronavirus indicating person-to-person transmission: A study of a family cluster. The Lancet, 395(10223): 514–523. Chen D, Xu W, Lei Z, Huang Z, Liu J, Gao Z, et al. (2020a). Recurrence of positive SARS-CoV-2 RNA in COVID-19: A case report. International Journal of Infectious Diseases, 93: 297–299. Chen J (2020). Pathogenicity and transmissibility of 2019-nCoV: A quick overview and comparison with other emerging viruses. Microbes and Infection, 22: 69–71. Chen N, Zhou M, Dong X, Qu J, Gong F, Han Y, et al. (2020b). Epidemiological and clinical characteristics of 99 cases of 2019 novel coronavirus pneumonia in Wuhan, China: A descriptive study. The Lancet, 395(10223): 507–513. Chib S, Greenberg E (1995). Understanding the metropolis-hastings algorithm. The American Statistician, 49(4): 327–335. Conceição KS, Andrade MG, Louzada F (2013). Zero-modified Poisson model: Bayesian approach, influence diagnostics, and an application to a Brazilian leptospirosis notification data. Biometrical Journal, 55(5): 661–678. Desta F, Mac Siurtain MP, Colbert JJ (1999). Parameter estimation of nonlinear growth models in forestry. Silva Fennica, 33(4): 327–336. Dorndorf A, Kargoll B, Paffenholz JA, Alkhatib H (2019). A bayesian nonlinear regression model based on t-distributed errors. In: IX Hotine0-Marussi Symposium on Mathematical Geodesy (P Novák, M Crespi, N Sneeuw, F Sansò, eds.), 127–135. Springer, Berlin. Engle RF (1982). Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation. Econometrica, 50(4): 987–1007. Engle RF (1983). Estimates of the variance of US inflation based upon the ARCH model. Journal of Money, Credit and Banking, 15(3): 286–301. Ferretti L, Wymant C, Kendall M, Zhao L, Nurtay A, Abeler-Dörner L, et al. (2020). Quantifying SARS-CoV-2 transmission suggests epidemic control with digital contact tracing. Science, 368(6491): 1–7. Gelfand AE, Dey DK, Chang H (1992). Model determination using predictive distributions with implementation via sampling-based methods (with discussion). Technical Report 462, Department of Statistics, Stanford University, Stanford, California. Geweke J (1992). Evaluating the accuracy of sampling-based approaches to the calculations of posterior moments. Bayesian statistics, 4: 641–649. Girardi P, Greco L, Mameli V, Musio M, Racugno W, Ruli E, et al. (2020). Robust inference for nonlinear regression models from the Tsallis score: Application to COVID-19 contagion in Italy. ArXiv preprint: https://doi.org/10.1002/sta4.309. Gupta RD, Kundu D (2001). Generalized exponential distribution: Different method of estimations. Journal of Statistical Computation and Simulation, 69(4): 315–337. Han Q, Lin Q, Jin S, You L (2020). Coronavirus 2019-nCoV: A brief perspective from the front line. Journal of Infection, 80(4): 373–377. Huang C, Wang Y, Li X, Ren L, Zhao J, Hu Y, et al. (2020). Clinical features of patients infected with 2019 novel coronavirus in Wuhan, China. The Lancet, 395(10223): 497–506. Ju B, Zhang Q, Ge X, Wang R, Yu J, Shan S, et al. (2020). Potent human neutralizing antibodies elicited by SARS-CoV-2 infection. BioRxiv preprint: https://doi.org/10.1101/2020.03.21.990770. Kandel N, Chungong S, Omaar A, Xing J (2020). Health security capacities in the context of COVID-19 outbreak: An analysis of International Health Regulations annual report data from 182 countries. The Lancet, 395: 1047–1053. Katz D, Azen S, Schumitzky A (1981). Bayesian approach to the analysis of nonlinear models: Implementation and evaluation. Biometrics, 37: 137–142. Kermack WO, McKendrick AG (1927). A contribution to the mathematical theory of epidemics. Proceedings of the Royal Society of London. Series A, 115(772): 700–721. Kim S, Kim H (2016). A new metric of absolute percentage error for intermittent demand forecasts. International Journal of Forecasting, 32(3): 669–679. Kim YI, Kim SG, Kim SM, Kim EH, Park SJ, Yu KM, et al. (2020). Infection and rapid transmission of SARS-CoV-2 in ferrets. Cell Host & Microbe, 27(5): 704–709. Kulikov VS (2001). Rational function. In: Encyclopedia of Mathematics (M Hazewinkel, ed.). http://encyclopediaofmath.org/index.php?title=Rational_function&oldid=48438. Lai CC, Shih TP, Ko WC, Tang HJ, Hsueh PR (2020). Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) and corona virus disease-2019 (COVID-19): The epidemic and the challenges. International Journal of Antimicrobial Agents, 55(3): 1–9. Lam TTY, Jia N, Zhang YW, Shum MHH, Jiang JF, Zhu HC, et al. (2020). Identifying SARS-CoV-2-related coronaviruses in Malayan pangolins. Nature, 583: 282–285. Lan J, Ge J, Yu J, Shan S, Zhou H, Fan S, et al. (2020). Structure of the SARS-CoV-2 spike receptor-binding domain bound to the ACE2 receptor. Nature, 581: 215–220. Li JY, You Z, Wang Q, Zhou ZJ, Qiu Y, Luo R, et al. (2020). The epidemic of 2019-novel-coronavirus (2019-nCoV) pneumonia and insights for emerging infectious diseases in the future. Microbes and Infection, 22(2): 80–85. Lili Wang YZ, Jie He BZ, Wang F, Lu Tang MK, Barker D, Eisenberg MC, et al. (2020). An epidemiological forecast model and software assessing interventions on the COVID-19 epidemic in China (with discussion). Journal of Data Science, 18(3): 409–432. Lu R, Zhao X, Li J, Niu P, Yang B, Wu H, et al. (2020). Genomic characterisation and epidemiology of 2019 novel coronavirus: Implications for virus origins and receptor binding. The Lancet, 395(10224): 565–574. Luo J (2020). Predictive monitoring of COVID-19. White paper, Singapore University of Technology. Lupia T, Scabini S, Pinna SM, Di Perri G, De Rosa FG, Corcione S (2020). 2019-novel coronavirus outbreak: A new challenge. Journal of Global Antimicrobial Resistance, 21: 22–27. McCulloch RE (1989). Local model influence. Journal of the American Statistical Association, 84(406): 473–478. Petrescu E (2009). A statistical distribution useful in product life cycle modeling. Management and Marketing, 4(2): 165–170. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (2007). Cambridge University Press, New York. Pung R, Chiew CJ, Young BE, Chin S, Chen MI, Clapham HE, et al. (2020). Investigation of three clusters of COVID-19 in Singapore: Implications for surveillance and response measures. The Lancet, 395(10229): 1039–1046. R Core Team (2020). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Ratkowsky DA (1983). Nonlinear Regression Modelling: A Unified Practical Approach. Marcel Dekker, New York. Schwarz G (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2): 461–464. Shang J, Ye G, Shi K, Wan Y, Luo C, Aihara H, et al. (2020). Structural basis of receptor recognition by SARS-CoV-2. Nature, 581: 221–224. Shen C, Wang Z, Zhao F, Yang Y, Li J, Yuan J, et al. (2020). Treatment of 5 critically ill patients with COVID-19 with convalescent plasma. JAMA, 323(16): 1582–1589. Shereen MA, Khan S, Kazmi A, Bashir N, Siddique R (2020). Covid-19 infection: Origin, transmission, and characteristics of human coronaviruses. Journal of Advanced Research, 24: 91–98. Sohrabi C, Alsafi Z, O’Neill N, Khan M, Kerwan A, Al-Jabir A, et al. (2020). World health organization declares global emergency: A review of the 2019 novel coronavirus (covid-19). International Journal of Surgery, 76: 71–76. Sonnino G (2020). Dynamics of the COVID-19 comparison between the theoretical predictions and the real data. ArXiv preprint: https://arxiv.org/abs/2003.13540. Tsallis C, Tirnakli U (2020). Predicting COVID-19 peaks around the world. Frontiers in Physics, 8: 217. Tsay RS (2010). Analysis of Financial Time Series. John Wiley & Sons, New Jersey, 3 edition. Wan Y, Shang J, Graham R, Baric RS, Li F (2020). Receptor recognition by the novel coronavirus from Wuhan: An analysis based on decade-long structural studies of SARS coronavirus. Journal of virology, 94(7): 1–9. Wölfel R, Corman VM, Guggemos W, Seilmaier M, Zange S, Müller MA, et al. (2020). Virological assessment of hospitalized patients with COVID-2019. Nature, 581(7809): 465–469. World Health Organization (2020a). Coronavirus disease (COVID-19) pandemic. https://www.who.int/health-topics/coronavirus#tab=tab_1. World Health Organization (2020b). Coronavirus disease (COVID-19) pandemic. https://www.who.int/emergencies/diseases/novel-coronavirus-2019. World Health Organization (2020c). Coronavirus disease (COVID-19): Situation reports. https://www.who.int/emergencies/diseases/novel-coronavirus-2019/situation-reports. World Health Organization (2020d). Laboratory testing strategy recommendations for COVID-19: Interim guidance. https://www.who.int/publications/i/item/laboratory-testing-strategy-recommendations-for-covid-19-interim-guidance. Wu A, Peng Y, Huang B, Ding X, Wang X, Niu P, et al. (2020). Genome composition and divergence of the novel coronavirus (2019-nCoV) originating in China. Cell Host & Microbe, 27(3): 325–328. Zhang X, Ma R, Wang L (2020). Predicting turning point, duration and attack rate of COVID-19 outbreaks in major western countries. Chaos, Solitons & Fractals, 92: 214–217. Zhao S, Lin Q, Ran J, Musa SS, Yang G, Wang W, et al. (2020). Preliminary estimation of the basic reproduction number of novel coronavirus (2019-nCoV) in China, from 2019 to 2020: A data-driven analysis in the early phase of the outbreak. International Journal of Infectious Diseases, 92: 214–217.