Italy extends lockdown amid hopes of turning corner
bbc.com
bbc.com
Some back of the envelope math for Lombardy, the hardest hit region:
Total population ~ 10M
Total deaths (2020/3/30) = 4773
If one assumes an Infection Fatality Rate of 1% then we would have had 500k cases in the region about two weeks ago. Assuming a doubling of the cases every 5 days, this means that the current actual number of infections stands at 4M and it would take log2(10/4) = 1.3 new doublings to reach saturation: about a week.
Taking instead an IFR of 2% and doubling every 7 weeks, we'd have about 3 weeks left to herd immunity.
Of course one should take into account the fact that at some point this will stop behaving like an exponential and look more like a sigmoid, but herd immunity doesn't need 100% infection, so the orders of magnitude involved should be more or less the same.
This seems to be roughly consistent with what some more authoritative sources are saying for example [0] claims Italy is probably missing 95% of cases.
[0] https://cmmid.github.io/topics/covid19/severity/global_cfr_e...