There are tags already used for opening_hours or delivery specific for the COVID-19 virus, but I don’t see how to map (and how this could be useful) such different and evolving types of “closures” for entire countries.
People in Italy so far cannot move IF they don’t have specific reasons (work, health, buy food), and they have to wear masks and gloved, and stay 1m away from each other… None of these elements, in my opinion, can and should be mapped in OSM.
On the other hand, parks are closed, many (but not all) shops are closed to the public (but maybe they can deliver food), others changed opening hours. All these elements need specific detailed mapping, and in some cases, this is happening.
You can maybe tag entire Italy as “closed” for COVID, but it’s not really so, and different regions in Italy have slightly different rules.
I guess similar complications exist in other countries…
Ale