  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 on the
stochastic evolution of the state (e.g., to compute probability that the
hospital beds will reach a fill level, or that a specified percentage of the
population will die). If the control policy is not given, it is possible to
apply POMDP techniques to identify an optimal control policy that fulfils some
specified probabilistic goals. Whilst the paper primarily aims at the model
description, we show with numeric examples some of its potential applications.
