It would be nice to see the Italian numbers coming down faster (although they do seem to be stable now).
They have been in lockdown since the 10th so, if you assume an incubation period of 5-6 days and that people present at a hospital at t+7, then those from the worst infectivity rate should have presented about the 23rd.
From then on, although starting from a higher base, the infectivity rate should fall off a cliff and new infections should initially rise more slowly or stabilise and then collapse. The key is showing that the new infectivity rate is less than 1.
If, during lockdown, one case infects 0.75 new cases (or every 4 infects 3), then the half life would be 12 days (based on 5 day incubation). So every 5 days the number of new infections should halve. If you start at 10,000 and release the lockdown at 200 new cases, then you need about 5-6 half life’s of 60-72 days.
On the above basis, which is subject to huge assumptions, you would imagine a lockdown of 2-3 months.
The Italian numbers over the next week will be very informative.