A virulent disease is one that's infectious, spreading, and making lots of people sick, while a virulent rant is just a verbal attack, causing sickness of the emotional kind. Either way, something virulent puts a strain on the people who get it.
Two meanings come out of the roots for virulent: one being "poisonous" and the other, "spiteful." The virus-carrying meaning of virulent often gets combined with strain, such as in a "virulent strain of the flu." Those who aren’t carrying disease but are still considered virulent most likely lash out at others with a biting tone. Unleashing acid-tongued words on someone would be considered a virulent attack.