How do viruses replicate so quickly inside a host cell?

Question

Hello,

How does viral DNA "force" the cell to make so many copies of itself in such little time? Is it some kind of super-promoter? Is there a type of virus that does not have this mechanism making it so that the cell only produces a few (perhaps only about 10, a very small number) viruses per day?

Please help

I didn't find the right solution from the internet.

References:

http://www.askabiologist.org.uk/answers/viewtopic.php?id=12406

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Thank you