  The outbreak of COVID-19 in 2020 has led to a surge in interest in the
mathematical modeling of infectious diseases. Such models are usually defined
as compartmental models, in which the population under study is divided into
compartments based on qualitative characteristics, with different assumptions
about the nature and rate of transfer across compartments. Though most commonly
formulated as ordinary differential equation (ODE) models, in which the
compartments depend only on time, recent works have also focused on partial
differential equation (PDE) models, incorporating the variation of an epidemic
in space. Such research on PDE models within a Susceptible, Infected, Exposed,
Recovered, and Deceased (SEIRD) framework has led to promising results in
reproducing COVID-19 contagion dynamics. In this paper, we assess the
robustness of this modeling framework by considering different geometries over
more extended periods than in other similar studies. We first validate our code
by reproducing previously shown results for Lombardy, Italy. We then focus on
the U.S. state of Georgia and on the Brazilian state of Rio de Janeiro, one of
the most impacted areas in the world. Our results show good agreement with
real-world epidemiological data in both time and space for all regions across
major areas and across three different continents, suggesting that the modeling
approach is both valid and robust.
