'over' in 'over the last few years'

Over the last few years we have seen a sudden increase in the number of cases of food poisoning.

Russian top officials predict trade figure could tripple [/b]over[/b] the next five years.

If 'over' in these cases means 'during' as dictionary says, which sense of 'during' is appropriate? Is it the 'throughout' during or is it the at-one-point-in the-course-of during?

In that Russian trade sentence, the first sense seems not fit, but the second sense appears to be awkward, too. Are Russian official literally saying that trade figures will precisely tripple at some certain moment within the next five years?

Thanks!

In that context, 'over' refers to the entire span of time (e.g., place the blanket over the bed so it covers the entire bed). 'over' umbrellas the entire period:

There have been a number of cases of food poisoning within the following span of time: some time inside the past two years.

Thanks!