This is a really small passage in Chapter Thirteen, and it's easy to miss if you're reading quickly. That being said, it's arguably the most skilled, artistic moment in Brave New World, partly because it's so minute. Huxley, for once, wasn't flagrantly obvious. He didn't beat us over the head, he just inserted a little anecdote and let it stand on its own.
Lenina, distraught by her unchecked and unsatisfied desire for John, gets flustered at work and accidentally misses giving one bottle its immunization against sleeping sickness. The story then halts for a minute while the narrative reveals this: "Twenty-two years, eight months, and four days from that moment, a promising young Alpha-Minus administrator at Mwanza-Mwanza was to die of trypanosomiasis – the first case for over half a century."
Beautiful. Look at the specificity on display here: ""Twenty-two years, eight months, and four days." Then Huxley uses "trypanosomiasis" instead of "sleeping sickness." He's really driving home the notion of scientific exactitude. This is the same sort of horrifying precision we saw in Chapter One, when the Director and Henry Foster outlined with a sickening barrage of numbers the way in which humans are created and grown. The difference is that here, the chain of cause and effect isn't effectively controlled by the human hand. After all, humans are fallible, so as exact and as rigid men like Mustapha might think their system is, there are always going to be errors, mistakes, and other minor disasters. So while this passage is horrifying, it's also hopeful, – Lenina, in making this error, has proven herself more human than machine.
But mostly, we're impressed with the fact that Huxley didn't tell us this in the subsequent paragraph, so maybe that's the real achievement here, gorgeous literary artistry aside.