The COVID-19 epidemic hit Italy particularly hard, yielding the implementation of strict national lockdown rules. Previous modelling studies at the national level overlooked the fact that Italy is divided into administrative regions which can independently oversee their own share of the Italian National Health Service. Here, we show that heterogeneity between regions is essential to understand the spread of the epidemic and to design effective strategies to control the disease. We model Italy as a network of regions and parameterize the model of each region on real data spanning over two months from the initial outbreak. We confirm the effectiveness at the regional level of the national lockdown strategy and propose coordinated regional interventions to prevent future national lockdowns, while avoiding saturation of the regional health systems and mitigating impact on costs. Our study and methodology can be easily extended to other levels of granularity to support policy- and decision-makers.
Network reciprocity has been successfully put forward (since M. A. Nowak and R. May’s, 1992, influential paper) as the simplest mechanism—requiring no strategical complexity—supporting the evolution of cooperation in biological and socioeconomic systems. The mechanism is actually the network, which makes agents’ interactions localized, while network reciprocity is the property of the underlying evolutionary process to favor cooperation in sparse rather than dense networks. In theoretical models, the property holds under imitative evolutionary processes, whereas cooperation disappears in any network if imitation is replaced by the more rational best-response rule of strategy update. In social experiments, network reciprocity has been observed, although the imitative behavior did not emerge. What did emerge is a form of conditional cooperation based on direct reciprocity—the propensity to cooperate with neighbors who previously cooperated. To resolve this inconsistency, network reciprocity has been recently shown in a model that rationally confronts the two main behaviors emerging in experiments—reciprocal cooperation and unconditional defection—with rationality introduced by extending the best-response rule to a multi-step predictive horizon. However, direct reciprocity was implemented in a non-standard way, by allowing cooperative agents to temporarily cut the interaction with defecting neighbors. Here, we make this result robust to the way cooperators reciprocate, by implementing direct reciprocity with the standard tit-for-tat strategy and deriving similar results.
Recently, it has been suggested that network temporality can be exploited to substantially reduce the energy required to control complex networks. This somewhat counterintuitive finding was explained through an evocative example of the advantage of temporal networks: when navigating a sailboat, we raise the sails when the wind helps us while lowering them when it works against us. Unfortunately, controlling complex networks inherits a further analogy with navigating a sailboat: having to face the inherent uncertainty of future winds. We rarely, if ever, have deterministic knowledge of the evolution of the network we want to control. Here, our challenge is to exploit the potential advantages of temporality when only a probabilistic description of the future is available. We prove that, in this more realistic setting, exploiting temporality is no more a panacea for network control, but rather an asset of a wider toolbox made available by the scientific community. One that can indeed turn out useful, provided that the temporality of the network structure matches the intrinsic time scales of the nodes we want to control.
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