  This paper is concerned with the design of intermittent non-pharmaceutical
strategies to mitigate the spread of the COVID-19 epidemic exploiting network
epidemiological models. Specifically, by studying a variational equation for
the dynamics of the infected in a network model of the epidemic spread, we
derive, using contractivity arguments, a condition that can be used to
guarantee that, in epidemiological terms, the effective reproduction number is
less than unity. This condition has three advantages: (i) it is easily
computable; (ii) it is directly related to the model parameters; (iii) it can
be used to enforce a scalability condition that prohibits the amplification of
disturbances within the network system. We then include satisfaction of such a
condition as a constraint in a Model Predictive Control problem so as to
mitigate (or suppress) the spread of the epidemic while minimizing the economic
impact of the interventions. A data-driven model of Italy as a network of three
macro-regions (North, Center, and South), whose parameters are identified from
real data, is used to illustrate and evaluate the effectiveness of the proposed
control strategy.
