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

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 ( R 0 )and the effective reproduction number ( R e ) 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 R 0 and the evolution of the effective reproduction number R e . 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...

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“…Finally, we zoomed in our analysis on the early stage of the epidemic. In agreement with [ 18 ], our model predicted an undetected–detected ratio of 10:1 on 24 February 2020, suggesting that COVID-19 might have been circulating in Italy, though unknown, far before the identification of the first case [ 19 , 20 ]. This hypothesis seems to be supported, among the others, by the presence of IgM/IgG antibodies against SARS-CoV-2 nucleocapsid protein in blood samples collected in Milan at the real beginning of the outbreak [ 21 ].…”

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“…Our localization of the day-zero of the Italian outbreak supports the existing chronology of the early outbreak in Italy with the first significant cluster of patients reported in the second half of February [8,9].…”

The first wave of the SARS-CoV-2 epidemic in Tuscany (Italy): A SI2R2D compartmental model with uncertainty evaluation

“…We use the average of this distribution as a fixed parameter in the calibration of the SI 2 R 2 D model; we use the entire distribution in the GSA. We highlight that the value of π is assumed to be constant over time under the assumptions that the COVID-19 testing policies always rely on the same symptom-based criteria and that the distribution of the symptoms does not change over time during the study period (see also Russo et al for a similar assumption [15]).…”

“…The interested reader can find an accurate description of the literature in [8]. Some of the proposed compartmental models explicitly account for the presence of undetected asymptomatic individuals, thus for the fact that part of the epidemic is submerged [9][10][11][12][13][14][15].…”