A simplified model for the analysis of COVID-19 evolution during the lockdown period in Italy

A simplified model applied to COVID-19 cases detected and officially published by the italian government [1], seems to fit quite well the time evolution of the disease in Italy during the period feb-24th - may-19th 2020. The hypothesis behind the model is based on the fact that in the lockdown period the infection cannot be transmitted due to social isolation and, more generally, due to the strong protection measures in place during the observation period. In this case a compartment model is used and the interactions between the different compartments are simplified. The sample of cases detected is intended as a set of individuals susceptible to infection which, after being exposed and undergoing the infection, were isolated ( treated) in such a way they can no longer spread the infection. The values obtained are to be considered indicative. The same model has been applied both to the data relating to Italy and to some regions of Italy (Lombardia, Piemonte, Lazio, Campania, Calabria, Sicilia, Sardegna), generally finding a good response and indicatively interesting values (see chap. 5). The only tuning parameter is the incubation period{tau} that, together with the calculated growth rate{kappa} of the exponential curve used to approximate the early stage data, in this modelization, are in strong relationship with the compartments transfer rates. In particular[R] 0 and the numerical value of{kappa} (dimensionless) in this model are linked by the relation:[R] 0 = 1/{kappa}2 Revision HistoryO_ST_ABSRevision # 1C_ST_ABSO_LIErrata corrige in section 1 (Introduction): the equations that summarize the relationship between the parameters were wrong. This revised version contains the correct equations at page 2. C_LIO_LIThe synchronization criteria is updated. No need to use a threshold different to the one used to determine the growth coefficient. The results are now updated with the synchronization point near to the 20% of the maximum value of the cases detected per day: O_FD O_INLINEFIG[Formula 1]C_INLINEFIGM_FD(1)C_FD C_LIO_LIModifications in section 4 (Model results for Italy). It is appropriate to use an exponential function instead of a logistic function to find the growth rate in the initial phase. Section 4 and the results are now updated. C_LIO_LISome non-substantial corrections in the descriptive part. C_LI Revision # 2O_LIErrata corrige in the system differential equation 6: in the the derivative of S were reported a wrong additional term N. Now the equation 6 is correct. C_LI