• cellular automaton
• COVID-19
• individual based model
• macroscopic limit

The goal of this work is to develop a mathematical model to analyze the spread of COVID-19 infection. The first part of this thesis concerns the relation between compartmental and individual based models. In particular, we will see how a model of the latter type leads to SIR model in a suitable macroscopic limit. In the second part we concentrate on the development of a model for the description of the spreading of COVID-19. We use a cellular automaton to model the outbreak, consisting of N individuals. We present different versions of the model, from the simplest to the most complicated one, in order to take into account the different social structures that characterize our society. We describe the relations between the parameters of our model and experimental quantities. Finally, to test how our model behaves, we concentrate on numerical simulations. We begin with the choice of the parameters and a comparison between the different versions of the model. We then concentrate on three important experimental quantities, incubation period, serial interval and R0, and we see how their values and their probability distributions, extrapolated from our model, compare to those we can find in the specific literature. In the end, we focus on the simulation of a real case and we explain why we think that randomness is a really important feature of the model.