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