Viruses are a little different, though. Retroviruses aside, viruses spread as much and as fast as possible; any mutation that makes them spread more slowly is crowded out, evolution style.

So long as it can spread between hosts well enough, a deadly virus is a very successful virus – up until it's driven its host species to local extinction.

The deadliness of a virus doesn't assist its spread. The deadliness doesn't make it more or less successful, everything else being equal, but usually dead hosts are hosts that don't continue to spread the virus, so things aren't equal. In most cases deadliness in viruses is selected out precisely in order to increase their spread.

Deadliness of the virus is just a side effect of its fast spread - the major part of the spread is replication which damages the host. The virus is an optimization problem - replicate and spread as fast as you can as long as the associated host damage and deaths result in the spread decrease smaller than the gain from the replication intensity increase causing that damage and deaths.

A game that you can play in simulation: https://en.wikipedia.org/wiki/Plague_Inc.