Tracing DAY-ZERO and Forecasting the Fade out of the COVID-19 Outbreak in Lombardy, Italy: A Compartmental Modelling and Numerical Optimization Approach
Authors: Russo Lucia , Anastassopoulou Cleo , Tsakris Athanasios , Bifulco Gennaro Nicola , Campana Emilio Fortunato , Toraldo Gerardo , Siettos Constantinos 
Published: March 2020

AbstractItaly currently constitutes the epicenter of the novel coronavirus disease (COVID-19) pandemic, having surpassed China’s death toll. The disease is sweeping through Lombardy, which remains in lockdown since the 8th of March. As of the same day, the isolation measures taken in Lombardy have been extended to the entire country. Here, we provide estimates for: (a) the DAY-ZERO of the outbreak in Lombardy, Italy; (b) the actual number of exposed/infected cases in the total population; (c) the basic reproduction number (R0); (d) the “effective” per-day disease transmission; and, importantly, (e) a forecast for the fade out of the outbreak, on the basis of the COVID-19 Community Mobility Reports released by Google on March 29.MethodsTo deal with the uncertainty in the number of actual exposed/ infected cases in the total population, we address a compartmental Susceptible/ Exposed/ Infectious/ Recovered/ Dead (SEIRD) model with two compartments of infectious persons: one modelling the total cases in the population and another modelling the confirmed cases. The parameters of the model corresponding to the recovery period, the time from the onset of symptoms to death, the case fatality ratio, 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-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 SEIRD simulator to fit the numbers of new daily cases from February 21 to the 8th of March, the lockdown day of Lombardy and of all Italy. This was accomplished by solving a mixed-integer optimization problem with the aid of genetic algorithms. Based on the computed values, we also provide an estimation of the basic reproduction number R0. Furthermore, based on an estimation for the reduction in the “effective” transmission rate of the disease as of March 8 that reflects the suspension of almost all activities in Italy, we ran the simulator to forecast the fade out of the epidemic. For this purpose, we considered the reduction in mobility in Lombardy as released on March 29 by Google COVID-19 Community Mobility Reports, the effect of social distancing, and the draconian measures taken by the government on March 20 and March 21, 2020.ResultsBased on the proposed methodological procedure, we estimated that the DAY-ZERO was most likely between January 5 and January 23 with the most probable date the 15th of January 2020. The actual cumulative number of exposed cases in the total population in Lombardy on March 8 was of the order of 15 times the confirmed cumulative number of infected cases. The “effective” per-day disease transmission rate for the period until March 8 was found to be 0.686 (95% CI:0.660, 0.713), while the basic reproduction number R0 was found to be 4.51 (95% CI: 4.14, 4.90).Importantly, simulations show that the COVID-19 pandemic in Lombardy is expected to fade out by the end of May -early June, 2020, if the draconian, as of March 20 and March 21, measures are maintained.