Well, we do have a contact-tracing app, but only a few million have downloaded it and I do know some people who have demonstrated a limitation in their mental capacity by getting all tinfoil-hat about the update to Android which implemented the relevant API.Three experts who spoke to the Guardian put this down to good surveillance and contact-tracing, as well as most of the population diligently following safety rules, with many people wearing face masks outside even though it is not mandatory.
I've actually been following the stats for Lombardy, Emilia-Romagna and Veneto, with Veneto showing a bit of a bump recently which already seems to be coming down again while Emilia-Romagna is steadily increasing albeit from a very low level. This while Lombardy is steadily decreasing. Overall nationwide it adds up to a slight increase over the past couple of weeks.
I think people in Lombardy are aware of how bad things really were and therefore mostly take these things seriously; I remember masks being worn even before they became mandatory, while the "civil protection" agency (in Rome) was saying that they were unnecessary or akshually counter-productive (but when the Chinese specialists arrived to help out, their first comment was "why isn't everyone wearing masks?")
It's possible that other regions of Italy, which avoided the same levels of contagion because the got locked down the day after Lombardy did just like the UK should have done, are taking it less seriously now.
My reason for following Emilia-Romagna is that it recently had more cases in a day than Lombardy did; I want to see if there's any effect of everyone going to the beach (and the associated nightlife). Also because a couple of weeks ago there were people here who hadn't actually read the regional ordinances assuming that Rimini was basically completely back to normal regarding dancing (to which people from there said, no it f.cking is not).
(My reason for following Veneto was that it had the first outbreak at roughly the same time as Lombardy did, if not before, but they dealt with it properly because the scientists ignored the WHO and managed to eventually convince the governor so things worked out much better for them.)