A Spectral Clustering Approach for the Evolution of the COVID-19 Pandemic in the State of Rio Grande do Sul, Brazil

L. E. Allem, C. Hoppen, M. M. Marzo, L. S. Sibemberg


The aim of this paper is to analyse the evolution of the COVID-19 pandemic in Rio Grande do Sul by applying graph-theoretical tools, particularly spectral clustering techniques, on weighted graphs defined on the set of 167 municipalities in the state with population 10,000 or more, which are based on data provided by government agencies and other sources. To respond to this outbreak, the state has adopted a system by which pre-determined regions are assigned flags on a weekly basis, and different measures go into effect according to the flag assigned. Our results suggest that considering a flexible approach to the regions themselves might be a useful additional tool to give more leeway to cities with lower incidence rates, while keeping the focus on public safety. Moreover, simulations show that the combination of pendulum migration and isolation data used in this paper leads to a coherent qualitative description of the evolution of the pandemic in Rio Grande do Sul. These simulations also confirm the dampening effect of isolation on the dissemination of the disease.


Spectral clustering, COVID-19 pandemic, discrete epidemiological model.

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DOI: https://doi.org/10.5540/tcam.2022.023.04.00705

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Trends in Computational and Applied Mathematics

A publication of the Brazilian Society of Applied and Computational Mathematics (SBMAC)


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