Iceland tested 12% of their population so they cannot be underestimating the positive cases that much. Their death rate is 0.5% over the tested positive. Same rate for UAE who tested 8% of the population. Let us say that they are underestimating cases by a factor 5: you end up with 0.1% mortality. If you can slow down the contagion to a constant rate and reach herd immunity in one year, it is < 0.1% population dying in 1 year on top of the 1.2% normal rate. In Italy it would be a toll of 60000 including 22000 already dead. With the present lockdown measures, the daily covid-19 deaths (today around 500/day) will be down to 200/day by May 4 when the lockdown should be relieved. If the lockdown were to indefinitely continue, rates would further drop and the extrapolation looks like death toll would stop at 30000. Should the reopening of the economy result in freezing the death rate at around 200/day, only gradually slowing down as we approach herd immunity, it may take little less than a year. It is a sad tradeoff (30000 lives) but the breakdown of economy may do as much damage. The gamble is on the real mortality figures.
ETA: looking at the timeline, UAE data are too recent to be trusted. But Iceland with a population of 300000 roughly, is well past its peak of active cases.