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The mathematical modeling of infectious diseases is a fundamental researchfield for the planning of strategies to contain outbreaks. The modelsassociated with this field of study usually have exponential prior assumptionsin the number of new cases, while the exploration of spatial data has beenlittle analyzed in these models. In this paper, we model the number of newcases of the Coronavirus Disease 2019 (COVID-19) as a problem of reconstructionof time-varying graph signals. To this end, we proposed a new method based onthe minimization of the Sobolev norm in graph signal processing. Our methodoutperforms state-of-the-art algorithms in two COVID-19 databases provided byJohns Hopkins University. In the same way, we prove the benefits of theconvergence rate of the Sobolev reconstruction method by relying on thecondition number of the Hessian associated with the underlying optimizationproblem of our method.

On the Minimization of Sobolev Norms of Time-Varying Graph Signals: Estimation of New Coronavirus Disease 2019 Cases