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

Lucia Russo; Cleo Anastassopoulou; Athanassios Tsakris; Gennaro Nicola Bifulco; Emilio Fortunato Campana; Gerardo Toraldo; Constantinos Siettos

In an attempt to assess the dynamics of the outbreak for forecasting pur- 30 poses, as well as to estimate epidemiological parameters that cannot be computed directly based on clinical data, such as the transmission rate of the disease and the basic reproduction number, R 0 , defined as the expected number of exposed cases generated by one infected case in a population where all individuals are susceptible, many mathematical modelling studies have already appeared 35 since the first confirmed COVID-19 case. The first models mainly focused on the estimation of the basic reproduction number R 0 using dynamic mechanistic mathematical models ( [4, 5, 6, 7] ), but also simple exponential growth models (see e.g. [8, 9] ). Compartmental epidemiological models like SIR, SIRD, SEIR and SEIRD have been proposed to estimate other important epidemiological 40 parameters, such as the transmission rate and for forecasting purposes (see e.g. [7, 10] ). Other studies have used metapopulation models, which include data of human mobility between cities and/or regions to forecast the evolution of the outbreak in other regions/countries far from the original epicenter in China large percentage of asymptomatic or mildly symptomatic cases experiencing the disease like the common cold or the flu (see e.g. [14] ), and (b) the uncertainty regarding the DAY-ZERO of the outbreak, the knowledge of which is crucial to assess the stage and dynamics of the epidemic, especially during the first growth period. 55 To cope with the above problems, we herein propose a SEIRD with two compartments, one modelling the total infected cases in the population and another modelling the confirmed cases. The proposed modelling approach is applied to Lombardy, the epicenter of the outbreak in Italy, to estimate the scale of under-reporting of the number of actual cases in the total population, 60 the DAY-ZERO of the outbreak and for forecasting purposes. The above tasks were accomplished by the numerical solution of a mixed-integer optimization problem using the publicly available data of daily new cases for the period