In this thesis, we propose a Boltzmann-type kinetic approach in order to study the spread of an infectious disease. In particular, a mass-varying interacting multi-agent system is used to model a population and the confinement strategies that are adopted to stem the on-going epidemic in it, namely quarantine and vaccination. Every agent is characterized by a microscopic state, a “viral load”, and a label, that indicates the group the agent belongs to. The viral load changes as a consequence of interactions, while the label follows a Markov-type state dependent jump process. The quarantine strategy is firstly analyzed and the requirements for it to be effective outlined: a prompt isolation of the infected successfully stem the epidemic.