Hmmm, aren't we actually helping the deadly strains by putting a lot of effort in keeping those people alive? Those who usually would be dead, can actually survive nowadays, and that virus could somehow spread further?
Yeah maybe, but that's a pretty bleak point of view. "Sorry, you need to die so that this deadly variety can't continue to spread." I think we'd all rather give a fighting chance to anyone needing it using the best tools available.
Consider Smallpox. Smallpox ravaged humanity for thousands of years. Infected probably a billion people or more and you ended up with two subtypes. 90% of the infections were the more deadly type.
Explain how the virus could spread after they had recovered, a necessary step for which is their immune system clearing the virus.