Video report by ITV News Europe Editor James Mates
When the numbers dying stay stubbornly high, it is difficult to believe that things are getting better.
But when dealing with the spread of a virus, just stabilising the numbers of infections and deaths is a real sign of progress.
That seems to be happening now in both Spain and Italy, with the really good news in Italy that new coronavirus infections have fallen significantly in the last 24 hours.
It is a terrifyingly large number, but slightly lower than Sunday.
Talking to doctors there on Monday morning, there is a belief that they are "flattening the curve", that they are seeing fewer new patients, and that the lockdown is having an effect.
Flags fly at half-mast outside Madrid's Regional Government building as a minute of silence is held for victims of the outbreak:
Spain locked down several days after Italy, so real improvements there may lag behind the Italian ones.
Pictures emerging from inside Madrid’s hospital show scenes of unbelievable crowding and an intensive care system (massively expanded) still in danger of being overwhelmed.
The worst of the crisis has, so far, hit in the wealthy cities of Madrid and Barcelona.
I was told on Monday that doctors are very worried what will happen if some of the poorer areas of Spain get hit anything like as hard.
ITALY saw an identical death toll to Spain at 812, but the numbers of new infections has fallen to 4,050, well below Monday's figure of 5,217 and the lowest we have seen in 10 days.
A warning about both these numbers: deaths are a lagging indicator, reflecting the numbers being infected days, or even weeks, ago, and infection rates are highly dependent on who you are testing and where.
So caution as always.
There are now concerns, too, about a public health emergency - or even violent protests - in Italy’s dangerously overcrowded prison system.
HUNGARY is worrying all of Europe with its new emergency powers that enable the Government to rule by decree, without oversight or the need for elections, indefinitely.
Both the European Union and the Council of Europe have expressed their disquiet, and Amnesty International say that it “creates an indefinite and uncontrolled state of emergency and gives Viktor Orbán carte blanche to restrict human rights”.
SWEDEN is being watched very closely because of its decision to take a more laissez-faire attitude than anywhere else in Europe, choosing to follow the "herd immunity" path originally favoured by the British Government.
So far the numbers of deaths and infections (146 and 982) are on a par with Denmark (allowing for population size) but about double that of Finland and higher that in Norway.