Robustness analysis in an inter-cities mobility network: modeling municipal, state and federal initiatives as failures and attacks toward SARS-CoV-2 containment.

We present a robustness analysis of an inter-cities mobility complex network, motivated by the challenge of the COVID-19 pandemic and the seek for proper containment strategies. Brazilian data from 2016 are used to build a network with more than five thousand cities (nodes) and twenty-seven states with the edges representing the weekly flow of people between cities via terrestrial transports. Nodes are systematically isolated (removed from the network) either at random (failures) or guided by specific strategies (targeted attacks), and the impacts are assessed with three metrics: the number of components, the size of the giant component, and the total remaining flow of people. We propose strategies to identify which regions should be isolated first and their impact on people mobility. The results are compared with the so-called reactive strategy, which consists of isolating regions ordered by the date the first case of COVID-19 appeared. We assume that the nodes' failures abstract individual municipal and state initiatives that are independent and possess a certain level of unpredictability. Differently, the targeted attacks are related to centralized strategies led by the federal government in agreement with municipalities and states. Removing a node means completely restricting the mobility of people between the referred city/state and the rest of the network. Results reveal that random failures do not cause a high impact on mobility restraint, but the coordinated isolation of specific cities with targeted attacks is crucial to detach entire network areas and thus prevent spreading. Moreover, the targeted attacks perform better than the reactive strategy for the three analyzed robustness metrics.