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On stable parameter estimation and short-term forecasting with quantified uncertainty with application to COVID-19 transmission

  • Alexandra Smirnova EMAIL logo , Brian Pidgeon and Ruiyan Luo
Published/Copyright: April 7, 2022

Abstract

A novel optimization algorithm for stable parameter estimation and forecasting from limited incidence data for an emerging outbreak is proposed. The algorithm combines a compartmental model of disease progression with iteratively regularized predictor-corrector numerical scheme aimed at the reconstruction of case reporting ratio, transmission rate, and effective reproduction number. The algorithm is illustrated with real data on COVID-19 pandemic in the states of Georgia and New York, USA. The techniques of functional data analysis are applied for uncertainty quantification in extracted parameters and in future projections of new cases.

MSC 2010: 47J06; 65J20; 65L08

Award Identifier / Grant number: 1818886

Award Identifier / Grant number: 2011622

Funding statement: A. Smirnova was supported by NSF awards 1818886 and 2011622 (DMS Computational Mathematics).

References

[1] R. C. Aster, B. Borchers and C. H. Thurber, Parameter Estimation and Inverse Problems, Academic Press, New York, 2011. Search in Google Scholar

[2] A. Atkeson, K. Kopecky and T. Zha, Estimating and Forecasting Disease Scenarios for COVID-19 with an SIR Model, NBER Working Paper No. 27335, 2020, NBER Program(s): Economic Fluctuations and Growth. 10.3386/w27335Search in Google Scholar

[3] A. B. Bakushinsky and M. Y. Kokurin, Iterative Methods for Ill-Posed Operator Equations with Smooth Operators, Springer, Dordrecht, 2004. Search in Google Scholar

[4] G. Chowell, Fitting dynamic models to epidemic outbreaks with quantified uncertainty: A primer for parameter uncertainty, identifiability, and forecasts, Infect. Dis. Model. 2 (2019), 379–398. 10.1016/j.idm.2017.08.001Search in Google Scholar PubMed PubMed Central

[5] G. Chowell and H. Nishiura, Transmission dynamics and control of Ebola virus disease (EVD): A review, BMC Med. 12 (2014), 10.1186/s12916-014-0196-0. 10.1186/s12916-014-0196-0Search in Google Scholar PubMed PubMed Central

[6] G. Chowell, A. Tariq and J. M. Hyman, A novel sub-epidemic modeling framework for short-term forecasting epidemic waves, BMC Med. 17 (2019), Article ID 164. 10.1186/s12916-019-1406-6Search in Google Scholar PubMed PubMed Central

[7] B. Efron and R. Tibshirani, Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Statist. Sci. 1 (1986), 54–75. 10.1214/ss/1177013815Search in Google Scholar

[8] H. Engl, M. Hanke and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic, Dordecht, 1996. 10.1007/978-94-009-1740-8Search in Google Scholar

[9] G. Giordano, F. Blanchini, R. Bruno, P. Colaneri, A. Di Filippo, A. Di Matteo and M. Colaneri, Modelling the COVID-19 epidemic and implementation of population-wide interventions in Italy, Nat. Med. 26 (2020), 855–860. 10.1038/s41591-020-0883-7Search in Google Scholar PubMed PubMed Central

[10] Q. Jin and W. Wang, Analysis of the iteratively regularized Gauss–Newton method under a heuristic rule, Inverse Problems 34 (2018), no. 3, Article ID 035001. 10.1088/1361-6420/aaa0fbSearch in Google Scholar

[11] B. Kaltenbacher, A. Neubauer and O. Scherzer, Iterative Regularization Methods for Nonlinear Ill-Posed Problems, Radon Ser. Comput. Appl. Math. 6, Walter de Gruyter, Berlin, 2008. 10.1515/9783110208276Search in Google Scholar

[12] J. O. Lloyd-Smith, S. Funk, A. R. McLean, S. Riley and J. L. Wood, Nine challenges in modelling the emergence of novel pathogens, Epidemics 10 (2015), 35–39. 10.1016/j.epidem.2014.09.002Search in Google Scholar PubMed PubMed Central

[13] S. Morse, J. Mazet, M. Woolhouse, C. Parrish, D. Carroll, W. Karesh and P. Daszak, Prediction and prevention of the next pandemic zoonosis, The Lancet 380 (2012), 1956–1965. 10.1016/S0140-6736(12)61684-5Search in Google Scholar PubMed PubMed Central

[14] A. Neubauer, Optimal convergence rates for inexact Newton regularization with CG as inner iteration, J. Inverse Ill-Posed Probl. 28 (2020), 145–153. 10.1515/jiip-2019-0092Search in Google Scholar

[15] J. Nocedal and S. Wright, Numerical Optimization, Springer, Cham, 2000. 10.1007/b98874Search in Google Scholar

[16] J. M. Ortega and W. C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, New York, 2014. Search in Google Scholar

[17] J. O. Ramsay, S. Graves and G. Hooker, FDA: Functional Data Analysis. R package version 5.1.4., 2020, https://CRAN.R-project.org/package=fda. Search in Google Scholar

[18] J. O. Ramsay and B. W. Silverman, Functional Data Analysis, Springer, Cham, 2005. 10.1007/b98888Search in Google Scholar

[19] E. O. Romero-Severson, N. Hengartner, G. Meadors and R. Ke, Change in global transmission rates of COVID-19 through May 6, PLoS ONE 15 (2020), no. 8, Article ID e0236776. 10.1371/journal.pone.0236776Search in Google Scholar

[20] K. Roosa, Y. Lee, R. Luo, A. Kirpich, R. Rothenberg, J. M. Hyman, P. Yan and G. Chowell, Short-term Forecasts of the COVID-19 Epidemic in Guangdong and Zhejiang, J. Clin. Med. 9 (2020), Article ID 596. 10.3390/jcm9020596Search in Google Scholar PubMed PubMed Central

[21] A. Smirnova, On convergence rates for iteratively regularized procedures with a linear penalty term, Inverse Problems 28 (2012), no. 8, Article ID 085005. 10.1088/0266-5611/28/8/085005Search in Google Scholar

[22] A. Smirnova and A. Bakushinsky, On iteratively regularized predictor-corrector algorithm for parameter identification, Inverse Problems 36 (2020), Article ID 125015. 10.1088/1361-6420/abc530Search in Google Scholar

[23] A. Smirnova, G. Chowell, L. DeCamp, S. Moghadas and M. Sheppard, Improving epidemic size prediction through stable reconstruction of disease parameters by reduced iteratively regularized Gauss–Newton algorithm, J. Inverse Ill-Posed Probl. 25 (2017), no. 5, 653–668. 10.1515/jiip-2016-0053Search in Google Scholar

[24] A. Smirnova, R. Renaut and T. Khan, Convergence and application of a modified iteratively regularized Gauss–Newton algorithm, Inverse Problems 23 (2007), no. 4, 1547–1563. 10.1088/0266-5611/23/4/011Search in Google Scholar

[25] R. N. Thompson, Epidemiological models are important tools for guiding COVID-19 interventions, BMC Med. 18 (2020), 10.1186/s12916-020-01628-4. 10.1186/s12916-020-01628-4Search in Google Scholar PubMed PubMed Central

[26] A. N. Tikhonov, A. Goncharsky, V. V. Stepanov and A. G. Yagola, Numerical Methods for the Solution of Ill-Posed Problems, Math. Appl. 328, Springer, Cham, 1995. 10.1007/978-94-015-8480-7Search in Google Scholar

[27] V. V. Vasin and A. L. Ageev, Ill-Posed Problems with A Priori Information, VNU, Utrecht, 1995. 10.1515/9783110900118Search in Google Scholar

[28] J. Weitz and J. Dushoff, Modeling Post-death Transmission of Ebola: Challenges for Inference and Opportunities for Control, Sci. Rep. 5 (2015), Article ID 8751. 10.1038/srep08751Search in Google Scholar PubMed PubMed Central

[29] F. Werner and B. Hofmann, Convergence analysis of (statistical) inverse problems under conditional stability estimates, Inverse Problems 36 (2020), Article ID 015004. 10.1088/1361-6420/ab4cd7Search in Google Scholar

[30] CDC Coronavirus (COVID-19): Symptoms of Coronavirus, https://www.cdc.gov/coronavirus/2019-ncov/symptoms-testing/symptoms.html. Search in Google Scholar

[31] Georgia Department of Public Health Daily Status Report https://dph.georgia.gov/covid-19-daily-status-report. Search in Google Scholar

[32] Trends in Number of COVID-19 Cases and Deaths in the US Reported to CDC, by State/Territory, https://covid.cdc.gov/covid-data-tracker/\#trends-totalandratecases. Search in Google Scholar

[33] U.S. Census Bureau, https://www.census.gov/quickfacts/GA. Search in Google Scholar

[34] U.S. Census Bureau, https://www.census.gov/quickfacts/NY. Search in Google Scholar

[35] WHO COVID-19 Global literature on coronavirus disease, https://search.bvsalud.org/global-literature-on-novel-coronavirus-2019-ncov/. Search in Google Scholar

[36] WHO Coronavirus Disease (COVID-19) Dashboard, https://covid19.who.int/. Search in Google Scholar

Received: 2021-06-22
Revised: 2022-02-02
Accepted: 2022-03-07
Published Online: 2022-04-07
Published in Print: 2022-12-01

© 2022 Walter de Gruyter GmbH, Berlin/Boston

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