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Tracing day-zero and forecasting the COVID-19 outbreak in Lombardy, Italy: A compartmental modelling and numerical optimization approach

Author

Listed:
  • Lucia Russo
  • Cleo Anastassopoulou
  • Athanasios Tsakris
  • Gennaro Nicola Bifulco
  • Emilio Fortunato Campana
  • Gerardo Toraldo
  • Constantinos Siettos

Abstract

Introduction: Italy became the second epicenter of the novel coronavirus disease 2019 (COVID-19) pandemic after China, surpassing by far China’s death toll. The disease swept through Lombardy, which remained in lockdown for about two months, starting from the 8th of March. As of that day, the isolation measures taken in Lombardy were extended to the entire country. Here, assuming that effectively there was one case “zero” that introduced the virus to the region, we provide estimates for: (a) the day-zero of the outbreak in Lombardy, Italy; (b) the actual number of asymptomatic infected cases in the total population until March 8; (c) the basic (R0)and the effective reproduction number (Re) based on the estimation of the actual number of infected cases. To demonstrate the efficiency of the model and approach, we also provide a tentative forecast two months ahead of time, i.e. until May 4, the date on which relaxation of the measures commenced, on the basis of the COVID-19 Community Mobility Reports released by Google on March 29. Methods: To deal with the uncertainty in the number of the actual asymptomatic infected cases in the total population Volpert et al. (2020), we address a modified compartmental Susceptible/ Exposed/ Infectious Asymptomatic/ Infected Symptomatic/ Recovered/ Dead (SEIIRD) model with two compartments of infectious persons: one modelling the cases in the population that are asymptomatic or experience very mild symptoms and another modelling the infected cases with mild to severe symptoms. The parameters of the model corresponding to the recovery period, the time from the onset of symptoms to death and the time from exposure to the time that an individual starts to be infectious, have been set as reported from clinical studies on COVID-19. For the estimation of the day-zero of the outbreak in Lombardy, as well as of the “effective” per-day transmission rate for which no clinical data are available, we have used the proposed SEIIRD simulator to fit the numbers of new daily cases from February 21 to the 8th of March. This was accomplished by solving a mixed-integer optimization problem. Based on the computed parameters, we also provide an estimation of the basic reproduction number R0 and the evolution of the effective reproduction number Re. To examine the efficiency of the model and approach, we ran the simulator to “forecast” the epidemic two months ahead of time, i.e. from March 8 to May 4. For this purpose, we considered the reduction in mobility in Lombardy as released on March 29 by Google COVID-19 Community Mobility Reports, and the effects of social distancing and of the very strict measures taken by the government on March 20 and March 21, 2020. Results: Based on the proposed methodological procedure, we estimated that the expected day-zero was January 14 (min-max rage: January 5 to January 23, interquartile range: January 11 to January 18). The actual cumulative number of asymptomatic infected cases in the total population in Lombardy on March 8 was of the order of 15 times the confirmed cumulative number of infected cases, while the expected value of the basic reproduction number R0 was found to be 4.53 (min-max range: 4.40- 4.65). On May 4, the date on which relaxation of the measures commenced the effective reproduction number was found to be 0.987 (interquartiles: 0.857, 1.133). The model approximated adequately two months ahead of time the evolution of reported cases of infected until May 4, the day on which the phase I of the relaxation of measures was implemented over all of Italy. Furthermore the model predicted that until May 4, around 20% of the population in Lombardy has recovered (interquartile range: ∼10% to ∼30%).

Suggested Citation

  • Lucia Russo & Cleo Anastassopoulou & Athanasios Tsakris & Gennaro Nicola Bifulco & Emilio Fortunato Campana & Gerardo Toraldo & Constantinos Siettos, 2020. "Tracing day-zero and forecasting the COVID-19 outbreak in Lombardy, Italy: A compartmental modelling and numerical optimization approach," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-22, October.
  • Handle: RePEc:plo:pone00:0240649
    DOI: 10.1371/journal.pone.0240649
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    References listed on IDEAS

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    1. Cleo Anastassopoulou & Lucia Russo & Athanasios Tsakris & Constantinos Siettos, 2020. "Data-based analysis, modelling and forecasting of the COVID-19 outbreak," PLOS ONE, Public Library of Science, vol. 15(3), pages 1-21, March.
    2. Joël Mossong & Niel Hens & Mark Jit & Philippe Beutels & Kari Auranen & Rafael Mikolajczyk & Marco Massari & Stefania Salmaso & Gianpaolo Scalia Tomba & Jacco Wallinga & Janneke Heijne & Malgorzata Sa, 2008. "Social Contacts and Mixing Patterns Relevant to the Spread of Infectious Diseases," PLOS Medicine, Public Library of Science, vol. 5(3), pages 1-1, March.
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    1. Sivakumaar, Vysaaly & Enayati, Shakiba & Shittu, Ekundayo, 2024. "Uncovering heterogeneous inequities induced by COVID-19 interventions: Evidence from three states in the U.S," Socio-Economic Planning Sciences, Elsevier, vol. 92(C).
    2. Elena Loli Piccolomini & Fabiana Zama, 2020. "Monitoring Italian COVID-19 spread by a forced SEIRD model," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-17, August.
    3. Roberto Antonietti & Paolo Falbo & Fulvio Fontini, 2023. "The Wealth of Nations and the First Wave of COVID-19 Diffusion," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 9(1), pages 61-83, March.
    4. Roberto Antonietti & Paolo Falbo & Fulvio Fontini & Rosanna Grassi & Giorgio Rizzini, 2021. "International Trade Network: Country centrality and COVID-19 pandemic," Papers 2107.14554, arXiv.org.

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