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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, we derive, using contractivity arguments, a condition that can be used to guarantee that the effective reproduction number is less than unity. This condition (i) is easily computable, (ii) is interpretable, being directly related to the model parameters, and (iii) 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.

Intermittent non-pharmaceutical strategies to mitigate the COVID-19 epidemic in a network model of Italy via constrained optimization