Tracing DAY-ZERO and Forecasting the Fade out of the COVID-19 Outbreak in Lombardy, Italy: A Compartmental Modelling and Numerical Optimization Approach.

Since the first suspected cluster of cases of coronavirus disease-2019 (COVID-19) on December 1st, 2019, in Wuhan, Hubei Province, China, a total of 195,892 confirmed infected cases, 80,840 recovered and 7,865 deaths have been reported worldwide up to March 16, 2020. After China, Italy is currently at the forefront of the combat against the epidemic that has now spread to all 22 Italian regions. 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. On March 11, the WHO declared COVID-19 pandemic. 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 mortality rates; and, importantly, (e) a forecast for the fade out of the outbreak, on the basis of the released data of confirmed cases for Lombardy from February 21 to March 8, the day of lockdown. Methods To deal with the uncertainty in the number of actual exposed/ infected cases in the total population, we address a new 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, 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 and mortality rates for which no clinical data are available, we have used the SEIRD simulator to fit the data 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, by reducing the estimated transmission rate by 90% on March 8 (to reflect the lockdown of almost all activities), we run the simulator from March 8 to forecast the fade out of the outbreak. Findings Based on the proposed methodological procedure, we estimated that 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. According to this scenario, the DAY-ZERO for the outbreak in Lombardy was the 21st of January 2020. The effective per-day disease transmission rate for the period until March 8 was found to be 0.779 (90% CI: 0.777-0.781), while the "effective" per-day mortality rate was found to be 0.0173 (90% CI: 0.0154-0.0192). Based on these values, the basic reproduction rate R0 was found to be 4.04 (90% CI: 4.03-4.05). Importantly, by reducing the transmission rate by 90% on March 8 to reflect the suspension of almost all activities in Italy, we run the simulator to forecast the fade out of the epidemic. Simulations show that if the measures continue, the complete fade out of the outbreak in Lombardy is expected to occur by the end of May 2020.