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

TL;DR

This paper develops a scalable, data-driven control strategy using network models and constrained optimization to implement intermittent non-pharmaceutical interventions, effectively reducing COVID-19 spread in Italy.

Contribution

It introduces a novel, easily computable condition for epidemic control within a network model and integrates it into a Model Predictive Control framework for intervention planning.

Findings

Effective reduction of COVID-19 spread in Italy's network model.

Control strategy minimizes economic impact while maintaining epidemic suppression.

Condition guarantees the effective reproduction number stays below one.

Abstract

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.