A SIDARTHE model is proposed to analyze the spread of SARS-CoV-2 in Italy. The model distinguishes between diagnosed and undiagnosed cases, as well as between different severity levels of infection. It accounts for the fact that undiagnosed individuals are more likely to spread the virus, as diagnosed individuals are typically isolated. The model also considers the impact of social distancing measures on the spread of the virus. The model is validated against real data from Italy, showing its ability to predict the epidemic's trajectory. The model's parameters are estimated based on data from February 20, 2020, to March 12, 2020. The model is used to simulate different scenarios of social distancing measures and their impact on the epidemic. The results show that strong social distancing measures can significantly reduce the number of infections and deaths. The model also highlights the importance of accurate diagnosis and the potential for misperception of the case fatality rate due to underdiagnosis. The model is a valuable tool for understanding the dynamics of the epidemic and for informing public health policies.A SIDARTHE model is proposed to analyze the spread of SARS-CoV-2 in Italy. The model distinguishes between diagnosed and undiagnosed cases, as well as between different severity levels of infection. It accounts for the fact that undiagnosed individuals are more likely to spread the virus, as diagnosed individuals are typically isolated. The model also considers the impact of social distancing measures on the spread of the virus. The model is validated against real data from Italy, showing its ability to predict the epidemic's trajectory. The model's parameters are estimated based on data from February 20, 2020, to March 12, 2020. The model is used to simulate different scenarios of social distancing measures and their impact on the epidemic. The results show that strong social distancing measures can significantly reduce the number of infections and deaths. The model also highlights the importance of accurate diagnosis and the potential for misperception of the case fatality rate due to underdiagnosis. The model is a valuable tool for understanding the dynamics of the epidemic and for informing public health policies.