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We examine the spatial modeling of the outbreak of COVID-19 in two regions:the autonomous community of Andalusia in Spain and the mainland of Greece. Westart with a 0D compartmental epidemiological model consisting of Susceptible,Exposed, Asymptomatic, (symptomatically) Infected, Hospitalized, Recovered, anddeceased populations. We emphasize the importance of the viral latent periodand the key role of an asymptomatic population. We optimize model parametersfor both regions by comparing predictions to the cumulative number of infectedand total number of deaths via minimizing the $\ell^2$ norm of the differencebetween predictions and observed data. We consider the sensitivity of modelpredictions on reasonable variations of model parameters and initialconditions, addressing issues of parameter identifiability. We model bothpre-quarantine and post-quarantine evolution of the epidemic by atime-dependent change of the viral transmission rates that arises in responseto containment measures. Subsequently, a spatially distributed version of the0D model in the form of reaction-diffusion equations is developed. We considerthat, after an initial localized seeding of the infection, its spread isgoverned by the diffusion (and 0D model "reactions") of the asymptomatic andsymptomatically infected populations, which decrease with the imposedrestrictive measures. We inserted the maps of the two regions, and we importedpopulation-density data into COMSOL, which was subsequently used to solvenumerically the model PDEs. Upon discussing how to adapt the 0D model to thisspatial setting, we show that these models bear significant potential towardscapturing both the well-mixed, 0D description and the spatial expansion of thepandemic in the two regions. Veins of potential refinement of the modelassumptions towards future work are also explored.

Reaction-diffusion spatial modeling of COVID-19: Greece and Andalusia as case examples