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A reaction-diffusion model was developed describing the spread of theCOVID-19 virus considering the mean daily movement of susceptible, exposed andasymptomatic individuals. The model was calibrated using data on the confirmedinfection and death from France as well as their initial spatial distribution.First, the system of partial differential equations is studied, then the basicreproduction number, R0 is derived. Second, numerical simulations, based on acombination of level-set and finite differences, shown the spatial spread ofCOVID-19 from March 16 to June 16. Finally, scenarios of unlockdown arecompared according to variation of distancing, or partially spatial lockdown.

A reaction-diffusion system to better comprehend the unlockdown:  Application of SEIR-type model with diffusion to the spatial spread of  COVID-19 in France