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The COVID-19 epidemic is the last of a long list of pandemics that have affected humankind in the last century. The SUITHER mathematical epidemiological model takes its name from the names of the seven compartments that it comprises: susceptible uninfected individuals (S), undetected (both asymptomatic and symptomatic) infected (U), isolated (I), hospitalized (H), threatened (T), extinct (E), and recovered (R). A suitable parameter calibration that is based on the combined use of least squares method and Markov Chain Monte Carlo (MCMC) method is implemented with the aim of reproducing the past history of the epidemic in Italy, surfaced in late February and still ongoing to date, and of validating SUIHTER in terms of its predicting capabilities. A distinctive feature of the new model is that it allows a one-to-one calibration strategy between the model compartments and the data that are daily made available from the Italian Civil Protection. The new model has been applied to the analysis of the Italian epidemic with emphasis on the second outbreak emerged in Fall 2020. From these results we can consider the epidemiological model SUIHTER as a suitable tool usable in a predictive manner to perform scenario analysis at national level.