Abstract
We propose a Markovian stochastic approach to model the spread of a SARS-CoV-2-like infection within a closed group of humans. The model takes the form of a Partially Observable Markov Decision Process (POMDP), whose states are given by the number of subjects in different health conditions. The model also exposes the different parameters that have an impact on the spread of the disease and the various decision variables that can be used to control it (e.g, social distancing, number of tests administered to single out infected subjects). The model describes the stochastic phenomena that underlie the spread of the epidemic and captures, in the form of deterministic parameters, some fundamental limitations in the availability of resources (hospital beds and test swabs). The model lends itself to different uses. For a given control policy, it is possible to verify if it satisfies an analytical property.