Design, validation, and analysis of a game-theoretic network epidemic model for COVID-19 spreading in Italy.

In the recent past, the world population has faced a very difficult period due to a globally widespread disease, known to all as COVID-19. This virus originated in China but then spread rapidly throughout the rest of the world, arriving in Italy at the end of February 2020 which was the beginning of some terrible months: COVID-19 positive individuals increased dramatically and hospitals, with their medical staff, had to endure unprecedented stress, not to forget also the huge number of deaths this epidemic caused. The government that was in charge at that time tried to limit the damage caused by this epidemic with a series of interventions and restrictive measures which were absolutely necessary to contain the spread of the virus, but on the other hand inevitably caused a difficult economic crisis causing discontent among a large part of the population: this is certainly a trouble, because the population is notoriously heterogeneous and it is not always possible to predict everyone’s behavior and reactions. At the state of the art were studied many epidemic models already before the spread of COVID-19, but very few of these deal with the aspect of people’s behavior as a dynamic that influences the spread of the epidemic. This master’s thesis aims to design two new epidemic models that also consider the behavior of people, with the design of specific payoff functions for a decision-making process based on game theory, in the first model to evaluate the choice of adopting self-protective behaviors like social distancing or wearing protective mask, while in the second model a decision on vaccination will also be added, which has been a delicate matter and discussed among people for a long time. Once this model has been created, it will be validated with a calibration of parameters and a validation based on the real data of infected and dead COVID-19 collected in Italy in recent years. After the validation of the model we will try to experiment through a control function new intervention policies by the government called NPI, or non-pharmaceutical interventions, with the aim of obviously reducing the number of infections and deaths to a minimum, being useful in the case of a future new pandemic that we all wish it would never happen again.