How do people avoid being replaced in "Invasion of the Body Snatchers"?

The 1956 original is creepy as hell, and the 1978 remake is somehow even bleaker (we don't talk about the remakes that came after that), but in all versions, one truth is constant. Just don't sleep. Ever. The alien plant spores fall from space and grow into giant seed pods that can duplicate any human placed near them. The catch is that the replication only works while you're asleep. Characters try popping amphetamines, but no amount of willpower, drugs, or terror can beat basic biology forever. Even just the idea of staying awake forever is making me exhausted, so my odds against an alien invasion are not great.