• COVID-19
• SIR
• SEIR
• epidemic modelling
• dynamical systems
• ODE
• Monte Carlo methods
• inference
• parameter identifiability

The COVID-19 pandemic evolution had an enormous impact on the scientific world, and a big effort has been devoted to making predictions on the pandemic evolution, using deterministic and stochastic modelling.
From the beginning of the pandemic, ``Protezione Civile'' has published daily reports providing information about the discovered infections and their conditions. With hospitalised individuals representing the population at death risk, particular attention has been given to modelling the evolution of the numbers of these cases.
The purpose of this thesis is to design and simulate models to depict the evolution of the epidemic. Using the database from ``Protezione Civile'', this work also tries to obtain via statistical inference the parameters driving the models used.
In order to achieve this aim, this work uses some results from both recent and non-recent literature, developing frameworks for modelling and, starting from standard methods in epidemiological inference, using statistical methodologies in order to obtain reliable estimates of parameters.
The models obtained in this study allow drawing some conclusions on the dynamics of future infections waves, with the possibility of modelling the evolution of the numbers of the worst cases. Further refinements and modifications of our models could prove very useful to help design more effective mitigation measures, to distinguish the most effective among them and to provide some indications on the healthcare needs.