Yes. This also works with epidemics. Die too quickly - less chance to infect others, being one man short makes your community poorer, which means fewer travelers, which also means less chance to infect other communities.

One reason Black Death led to so much witch hunting and jew burning and talk about divine punishment - many people were immune even when exposed to piles of bodies of infected, while those to get sick would die very fast. That's one way a highly deadly and quickly developing disease can survive, be deadly only to some part of the population. Well, rats and water too.