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  • Featured in Physics
  • Open Access

Modeling COVID-19 Dynamics in Illinois under Nonpharmaceutical Interventions

George N. Wong1,†, Zachary J. Weiner1,†, Alexei V. Tkachenko2, Ahmed Elbanna3, Sergei Maslov1,4,5,*, and Nigel Goldenfeld1,5,*

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 2Center for Functional Nanomaterials, Brookhaven National Laboratory, Upton, New York 11973, USA
  • 3Department of Civil Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 4Department of Bioengineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
  • 5Carl R. Woese Institute for Genomic Biology, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA

  • *Correspondence to: maslov@illinois.edu, nigel@illinois.edu.
  • †These authors contributed equally to this work.

Phys. Rev. X 10, 041033 – Published 16 November, 2020

DOI: https://doi.org/10.1103/PhysRevX.10.041033

Abstract

We present modeling of the COVID-19 epidemic in Illinois, USA, capturing the implementation of a stay-at-home order and scenarios for its eventual release. We use a non-Markovian age-of-infection model that is capable of handling long and variable time delays without changing its model topology. Bayesian estimation of model parameters is carried out using Markov chain Monte Carlo methods. This framework allows us to treat all available input information, including both the previously published parameters of the epidemic and available local data, in a uniform manner. To accurately model deaths as well as demand on the healthcare system, we calibrate our predictions to total and in-hospital deaths as well as hospital and ICU bed occupancy by COVID-19 patients. We apply this model not only to the state as a whole but also its subregions in order to account for the wide disparities in population size and density. Without prior information on nonpharmaceutical interventions, the model independently reproduces a mitigation trend closely matching mobility data reported by Google and Unacast. Forward predictions of the model provide robust estimates of the peak position and severity and also enable forecasting the regional-dependent results of releasing stay-at-home orders. The resulting highly constrained narrative of the epidemic is able to provide estimates of its unseen progression and inform scenarios for sustainable monitoring and control of the epidemic.

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Physics Subject Headings (PhySH)

Viewpoint

The Uncertain Future in How a Virus Spreads

Published 16 November, 2020

A new model helps clarify the limits of pandemic predictions, which are notoriously difficult for the near future and impossible for longer timescales.

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References (76)

  1. All executive orders related to COVID-19 issued by the State of Illinois Governor J. B. Pritzker are listed here: https://www2.illinois.gov/government/executive-orders. The timeline of COVID-19 mitigation in Illinois is summarized at https://en.wikipedia.org/wiki/COVID-19_pandemic_in_Illinois#Government_response.
  2. M. J. Keeling and P. Rohani, Modeling Infectious Diseases in Humans and Animals (Princeton University, Princeton, NJ, 2011).
  3. C. J. L. Murray, Forecasting COVID-19 Impact on Hospital Bed-Days, ICU-Days, Ventilator-Days and Deaths by US State in the Next 4 Months, medRxiv, 10.1101/2020.03.27.20043752.
  4. J. Ma, Estimating Epidemic Exponential Growth Rate and Basic Reproduction Number, Infect. Dis. Model. 5, 129 (2020).
  5. J. T. Wu, K. Leung, and G. M. Leung, Nowcasting and Forecasting the Potential Domestic and International Spread of the 2019-nCoV Outbreak Originating in Wuhan, China: A Modelling Study, Lancet 395, 689 (2020).
  6. C. Fraser, Estimating Individual and Household Reproduction Numbers in an Emerging Epidemic, PLoS One 2, e758 (2007).
  7. G. Chowell, Fitting Dynamic Models to Epidemic Outbreaks with Quantified Uncertainty: A Primer for Parameter Uncertainty, Identifiability, and Forecasts, Infectious Disease Modelling 2, 379 (2017).
  8. J. T. Wu, K. Leung, M. Bushman, N. Kishore, R. Niehus, P. M. de Salazar, B. J. Cowling, M. Lipsitch, and G. M. Leung, Estimating Clinical Severity of COVID-19 from the Transmission Dynamics in Wuhan, China, Nat. Med. 26, 506 (2020).
  9. C. Viboud, O. N. Bjørnstad, D. L. Smith, L. Simonsen, M. A. Miller, and B. T. Grenfell, Synchrony, Waves, and Spatial Hierarchies in the Spread of Influenza, Science 312, 447 (2006).
  10. J. O. Lloyd-Smith, S. J. Schreiber, P. E. Kopp, and W. M. Getz, Superspreading and the Effect of Individual Variation on Disease Emergence, Nature (London) 438, 355 (2005).
  11. M. Small, C. Tse, and D. M. Walker, Super-Spreaders and the Rate of Transmission of the SARS Virus, Physica D (Amsterdam) 215, 146 (2006).
  12. S. Bansal, B. T. Grenfell, and L. A. Meyers, When Individual Behaviour Matters: Homogeneous and Network Models in Epidemiology, J. R. Soc. Interface 4, 879 (2007).
  13. Y. Kim, H. Ryu, and S. Lee, Agent-Based Modeling for Super-Spreading Events: A Case Study of MERS-CoV Transmission Dynamics in the Republic of Korea, Int. J. Environ. Res. Public Health 15, 2369 (2018).
  14. Z. Dezső and A.-L. Barabási, Halting Viruses in Scale-Free Networks, Phys. Rev. E 65, 055103 (2002).
  15. K. Rock, S. Brand, J. Moir, and M. J. Keeling, Dynamics of Infectious Diseases, Rep. Prog. Phys. 77, 026602 (2014).
  16. R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani, Epidemic Processes in Complex Networks, Rev. Mod. Phys. 87, 925 (2015).
  17. W. O. Kermack and A. G. McKendrick, A Contribution to the Mathematical Theory of Epidemics, Proc. R. Soc. A 115, 700 (1927).
  18. J. Wallinga and M. Lipsitch, How Generation Intervals Shape the Relationship between Growth Rates and Reproductive Numbers, Proc. R. Soc. B 274, 599 (2007).
  19. R. A. Neher, R. Dyrdak, V. Druelle, E. B. Hodcroft, and J. Albert, Potential Impact of Seasonal Forcing on a SARS-CoV-2 Pandemic, Swiss Medical Weekly 150, 1112 (2020).
  20. A. Smirnova, L. deCamp, and G. Chowell, Forecasting Epidemics through Nonparametric Estimation of Time-Dependent Transmission Rates Using the SEIR Model, Bull. Math. Biol. 81, 4343 (2019).
  21. C. C. Ku, T.-C. Ng, and H.-H. Lin, Epidemiological Benchmarks of the COVID-19 Outbreak Control in China after Wuhan’s Lockdown: A Modelling Study with an Empirical Approach, SSRN Electron., 10.2139/ssrn.3544127 (2020).
  22. R. H. Mena, J. X. Velasco-Hernandez, N. B. Mantilla-Beniers, G. A. Carranco-Sapiéns, L. Benet, D. Boyer, and I. P. Castillo, Using the Posterior Predictive Distribution to Analyse Epidemic Models: COVID-19 in Mexico City, arXiv:2005.02294.
  23. M. Gatto, E. Bertuzzo, L. Mari, S. Miccoli, L. Carraro, R. Casagrandi, and A. Rinaldo, Spread and Dynamics of the COVID-19 Epidemic in Italy: Effects of Emergency Containment Measures, Proc. Natl. Acad. Sci. U.S.A. 117, 10484 (2020).
  24. R. Li, S. Pei, B. Chen, Y. Song, T. Zhang, W. Yang, and J. Shaman, Substantial Undocumented Infection Facilitates the Rapid Dissemination of Novel Coronavirus (SARS-CoV-2), Science 368, 489 (2020).
  25. H. Nishiura, N. M. Linton, and A. R. Akhmetzhanov, Serial Interval of Novel Coronavirus (COVID-19) Infections, Int. J. Infectious Diseases 93, 284 (2020).
  26. Z. Du, X. Xu, Y. Wu, L. Wang, B. J. Cowling, and L. A. Meyers, Serial Interval of COVID-19 among Publicly Reported Confirmed Cases, Emerg. Infect. Dis. 26, 1341 (2020).
  27. S. A. Lauer, K. H. Grantz, Q. Bi, F. K. Jones, Q. Zheng, H. R. Meredith, A. S. Azman, N. G. Reich, and J. Lessler, The Incubation Period of Coronavirus Disease 2019 (COVID-19) from Publicly Reported Confirmed Cases: Estimation and Application, Ann. Intern. Med. 172, 577 (2020).
  28. N. M. Linton, T. Kobayashi, Y. Yang, K. Hayashi, A. R. Akhmetzhanov, S.-m. Jung, B. Yuan, R. Kinoshita, and H. Nishiura, Incubation Period and Other Epidemiological Characteristics of 2019 Novel Coronavirus Infections with Right Truncation: A Statistical Analysis of Publicly Available Case Data, J. Clin. Med. 9, 538 (2020).
  29. R. Verity et al., Estimates of the Severity of Coronavirus Disease 2019: A Model-Based Analysis, Lancet Infect. Dis. (2020) [https://www.ncbi.nlm.nih.gov/pubmed/32240634].
  30. P. K. Bhatraju, B. J. Ghassemieh, M. Nichols, R. Kim, K. R. Jerome, A. K. Nalla, A. L. Greninger, S. Pipavath, M. M. Wurfel, L. Evans, P. A. Kritek, T. E. West, A. Luks, A. Gerbino, C. R. Dale, J. D. Goldman, S. O’Mahony, and C. Mikacenic, Covid-19 in Critically Ill Patients in the Seattle Region—Case Series, N. Engl. J. Med. (2020) [https://www.ncbi.nlm.nih.gov/pubmed/32227758].
  31. X. Yang, Y. Yu, J. Xu, H. Shu, J. Xia, H. Liu, Y. Wu, L. Zhang, Z. Yu, M. Fang, T. Yu, Y. Wang, S. Pan, X. Zou, S. Yuan, and Y. Shang, Clinical Course and Outcomes of Critically Ill Patients with SARS-CoV-2 Pneumonia in Wuhan, China: A Single-Centered, Retrospective, Observational Study, Lancet Resp. Med. 8, 475 (2020).
  32. ICNARC Report on COVID-19 in Critical Care, https://www.icnarc.org/Our-Audit/Audits/Cmp/Reports (2020).
  33. G. Meyerowitz-Katz and L. Merone, A Systematic Review and Meta-analysis of Published Research Data on COVID-19 Infection-Fatality Rates, medRxiv, 10.1101/2020.05.03.20089854.
  34. D. Foreman-Mackey, W. Farr, M. Sinha, A. Archibald, D. Hogg, J. Sanders, J. Zuntz, P. Williams, A. Nelson, M. de Val-Borro, T. Erhardt, I. Pashchenko, and O. Pla, emcee v3: A python Ensemble Sampling Toolkit for Affine-Invariant MCMC, J. Open Source Software 4, 1864 (2019).
  35. C. J. F. ter Braak and J. A. Vrugt, Differential Evolution Markov Chain with Snooker Updater and Fewer Chains, Stat. Comput. 18, 435 (2008).
  36. C. J. F. ter Braak, A Markov Chain Monte Carlo Version of the Genetic Algorithm Differential Evolution: Easy Bayesian Computing for Real Parameter Spaces, Stat. Comput. 16, 239 (2006).
  37. B. Farr, V. Kalogera, and E. Luijten, A More Efficient Approach to Parallel-Tempered Markov-Chain Monte Carlo for the Highly Structured Posteriors of Gravitational-Wave Signals, Phys. Rev. D 90, 024014 (2014).
  38. Data were downloaded from https://www.dph.illinois.gov/covid19/covid19-statistics.
  39. I. Korolev, Identification and Estimation of the SEIRD Epidemic Model for COVID-19, https://ssrn.com/abstract=3569367.
  40. M. Castro, S. Ares, J. A. Cuesta, and S. Manrubia, The Turning Point and End of an Expanding Epidemic Cannot Be Precisely Forecast, Proc. Natl. Acad. Sci. U.S.A. 117, 26190 (2020).
  41. W. C. Roda, M. B. Varughese, D. Han, and M. Y. Li, Why Is It Difficult to Accurately Predict the COVID-19 Epidemic?, Infectious Disease Modelling 5, 271 (2020).
  42. See map at https://www.dph.illinois.gov/sites/default/files/resources/ems-regions-map.pdf.
  43. S. J. Beckett, M. Dominguez-Mirazo, S. Lee, C. Andris, and J. S. Weitz, Spread of COVID-19 through Georgia, USA. Near-Term Projections and Impacts of Social Distancing via a Metapopulation Model, https://github.com/WeitzGroup/MAGEmodel_covid19_GA/blob/master/Report/GA_COVID19_assessment_21Apr2020.pdf.
  44. See https://www.blog.google/technology/health/covid-19-community-mobility-reports?hl=en.
  45. See https://www.unacast.com/post/rounding-out-the-social-distancing-scoreboard.
  46. S. Flaxman, S. Mishra, A. Gandy, H. Unwin, H. Coupland, T. Mellan et al., Report 13. Estimating the Number of Infections and the Impact of Non-pharmaceutical Interventions on COVID-19 in 11 European Countries (Imperial College, London, 2020).
  47. H. J. T. Unwin et al., Report 23: State-Level Tracking of COVID-19 in the United States WHO Collaborating Centre for Infectious Disease Modelling MRC Centre for Global Infectious Disease Analytics, 2020.
  48. S. Maslov and N. Goldenfeld, Window of Opportunity for Mitigation to Prevent Overflow of ICU Capacity in Chicago by COVID-19, https://www.medrxiv.org/content/early/2020/03/24/2020.03.20.20040048.
  49. D. H. Morris, F. W. Rossine, J. B. Plotkin, and S. A. Levin, Optimal, Near-Optimal, and Robust Epidemic Control, arXiv:2004.02209.
  50. J. Hellewell, S. Abbott, A. Gimma, N. I. Bosse, C. I. Jarvis, T. W. Russell, J. D. Munday, A. J. Kucharski, and R. M. Eggo, Feasibility of Controlling COVID-19 Outbreaks by Isolation of Cases and Contacts, The Lancet Global Health, 2020.
  51. L. Ferretti, C. Wymant, M. Kendall, L. Zhao, A. Nurtay, L. Abeler-Dorner, M. Parker, D. Bonsall, and C. Fraser, Quantifying SARS-CoV-2 Transmission Suggests Epidemic Control with Digital Contact Tracing, Science (2020) eabb6936 [https://www.ncbi.nlm.nih.gov/pubmed/32234805].
  52. Fitzhugh Mullan Institute for Health Workforce Equity and George Washington University, Contact Tracing Workforce Estimator, https://www.gwhwi.org/estimator-613404.html.
  53. I. Holmdahl and C. Buckee, Wrong but Useful—What Covid-19 Epidemiologic Models Can and Cannot Tell Us, New England J. Med., 10.1056/NEJMp2016822.
  54. K. D. Stärk, G. Regula, J. Hernandez, L. Knopf, K. Fuchs, R. S. Morris, and P. Davies, Concepts for Risk-Based Surveillance in the Field of Veterinary Medicine and Veterinary Public Health: Review of Current Approaches, BMC Health Services Res. 6, 20 (2006).
  55. A. Foddai, A. Lindberg, J. Lubroth, and J. Ellis-Iversen, Surveillance to Improve Evidence for Community Control Decisions During the COVID-19 Pandemic—Opening the Animal Epidemic Toolbox for Public Health, One Health 9, 100130 (2020).
  56. Data were downloaded from https://github.com/thecityny/covid-19-nyc-data.
  57. Data originally from https://www.thecity.nyc.
  58. Data were downloaded from https://github.com/nychealth/coronavirus-data.
  59. Y. Liu, R. M. Eggo, and A. J. Kucharski, Secondary Attack Rate and Superspreading Events for SARS-CoV-2, Lancet 395, e47 (2020).
  60. K. S. Raines, S. Doniach, and G. Bhanot, The Transmission of SARS-CoV-2 Is Likely Comodulated by Temperature and by Relative Humidity, https://www.medrxiv.org/content/early/2020/05/26/2020.05.23.20111278.
  61. R. E. Baker, W. Yang, G. A. Vecchi, C. J. E. Metcalf, and B. T. Grenfell, Susceptible Supply Limits the Role of Climate in the COVID-19 Pandemic, https://www.medrxiv.org/content/early/2020/04/07/2020.04.03.20052787.
  62. A. A. King, M. D. de Cellès, F. M. Magpantay, and P. Rohani, Avoidable Errors in the Modelling of Outbreaks of Emerging Pathogens, with Special Reference to Ebola, Proc. R. Soc. B 282, 0347 (2015).
  63. A. J. McKane and T. J. Newman, Predator-Prey Cycles from Resonant Amplification of Demographic Stochasticity, Phys. Rev. Lett. 94, 218102 (2005).
  64. T. Butler and N. Goldenfeld, Robust Ecological Pattern Formation Induced by Demographic Noise, Phys. Rev. E 80, 030902 (2009).
  65. D. Karig, K. M. Martini, T. Lu, N. A. DeLateur, N. Goldenfeld, and R. Weiss, Stochastic Turing Patterns in a Synthetic Bacterial Population, Proc. Natl. Acad. Sci. U.S.A. 115, 6572 (2018).
  66. G. Van Rossum and F. L. Drake, python3 Reference Manual (CreateSpace, Scotts Valley, CA, 2009).
  67. https://github.com/uiuc-covid19-modeling/pydemic.
  68. T. E. Oliphant, A Guide to NumPy (Trelgol Publishing, 2006), Vol. 1.
  69. P. Virtanen et al., SciPy 1.0: Fundamental Algorithms for Scientific Computing in python, Nat. Methods 17, 261 (2020).
  70. T. Pandas Development Team, pandas-dev/pandas: Pandas, 10.5281/zenodo.3509134.
  71. D. Foreman-Mackey, corner.py: Scatterplot Matrices in python, J. Open Source Software 24 (2016) [10.5281/zenodo.45906].
  72. J. D. Hunter, Matplotlib: A 2D Graphics Environment, Comput. Sci. Eng. 9, 90 (2007).
  73. Epidemiological Group of the New Coronavirus Pneumonia Emergency Response Mechanism of the China Center for Disease Control and Prevention, Epidemiological Characteristic Analysis of New Coronavirus Pneumonia, Chin. J. Epidemiol. 41, 145 (2020).
  74. K. Mizumoto, K. Kagaya, A. Zarebski, and G. Chowell, Estimating the Asymptomatic Proportion of Coronavirus Disease 2019 (COVID-19) Cases on Board the Diamond Princess Cruise Ship, Yokohama, Japan, 2020, Eurosurveillance 25, 10 (2020).
  75. H. Nishiura, T. Kobayashi, T. Miyama, A. Suzuki, S. Jung, K. Hayashi, R. Kinoshita, Y. Yang, B. Yuan, A. R. Akhmetzhanov, and N. M. Linton, Estimation of the Asymptomatic Ratio of Novel Coronavirus Infections (COVID-19), https://www.medrxiv.org/content/early/2020/02/17/2020.02.03.20020248.
  76. Data were downloaded from https://data.un.org.

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