A Markovian model for the spread of the SARS-CoV-2 virus

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.