  We present an early version of a
Susceptible-Exposed-Infected-Recovered-Deceased (SEIRD) mathematical model
based on partial differential equations coupled with a heterogeneous diffusion
model. The model describes the spatio-temporal spread of the COVID-19 pandemic,
and aims to capture dynamics also based on human habits and geographical
features. To test the model, we compare the outputs generated by a
finite-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 forecast
of the spatio-temporal COVID-19 spread in Lombardy and epidemiological data
collected at the municipality level. Additional simulations exploring
alternative scenarios for the relaxation of lockdown restrictions suggest that
reopening strategies should account for local population densities and the
specific dynamics of the contagion. Thus, we argue that data-driven simulations
of our model could ultimately inform health authorities to design effective
pandemic-arresting measures and anticipate the geographical allocation of
crucial medical resources.
