The explanation taken from my grammar book says
In a setence which includes a time clause with since, we generally prefer a past simple verb in the time clause and a present perfect verb in the main clause. The time clause refers to a particular point in the past.
- Since Mr Dodson became president unemployment has increased. (rather than ... has become...)
However, there's an exercise in another unit that says otherwise. This is a sentence in a problem in the unit and the words in bold is the key answer:
Correct the present perfect continuous verbs using either the past simple or present perfect.
It's remarkable to think that since 1950 influenza (1) has been claiming (has claimed) more than 50,000 lives in this country, and in 1957 alone around 6,000 people (2) have been dying (died).
As the book explains, then why not:
It's remarkable to think that since 1950 influenza claimed more than 50,000 lives in this country, and in 1957 alone around 6,000 people have died.