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We present an early version of aSusceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical modelbased on partial differential equations coupled with a heterogeneous diffusionmodel. The model describes the spatio-temporal spread of the COVID-19 pandemic,and aims to capture dynamics also based on human habits and geographicalfeatures. To test the model, we compare the outputs generated by afinite-element solver with measured data over the Italian region of Lombardy,which has been heavily impacted by this crisis between February and April 2020.Our results show a strong qualitative agreement between the simulated forecastof the spatio-temporal COVID-19 spread in Lombardy and epidemiological datacollected at the municipality level. Additional simulations exploringalternative scenarios for the relaxation of lockdown restrictions suggest thatreopening strategies should account for local population densities and thespecific dynamics of the contagion. Thus, we argue that data-driven simulationsof our model could ultimately inform health authorities to design effectivepandemic-arresting measures and anticipate the geographical allocation ofcrucial medical resources.

Simulating the spread of COVID-19 via spatially-resolved susceptible-exposed-infected-recovered-deceased (SEIRD) model with heterogeneous diffusion