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The aim of this paper is to analyse the evolution of the COVID-19 pandemic inRio Grande do Sul by applying graph-theoretical tools, particularly spectralclustering techniques, on weighted graphs defined on the set of 167municipalities in the state with population 10,000 or more, which are based ondata provided by government agencies and other sources. To respond to thisoutbreak, the state has adopted a system by which pre-determined regions areassigned flags on a weekly basis, and different measures go into effectaccording to the flag assigned. Our results suggest that considering a flexibleapproach to the regions themselves might be a useful additional tool to givemore leeway to cities with lower incidence rates, while keeping the focus onpublic safety. Moreover, simulations show the dampening effect of isolation onthe dissemination of the disease.

A spectral clustering approach for the evolution of the COVID-19 pandemic in the state of Rio Grande do Sul, Brazil