How did Lane's solution to the zombie problem in World War Z actually work?

Fair warning: this entire question is about the central plot point of the movie World War Z, and unavoidably spoils the film.

Lane's answer to the problem of zombies wanting to attack humans is to make each human terminally ill with a serious disease. He came up with the solution by observing zombies ignoring what ought to have been easy targets when those targets were weak. This doesn't seem like a viable long-term solution to me.

If the plan works as designed, then "camouflaged" humans will be safe from zombies, but will just die from the disease instead, which is no good. So the humans must also be given cures, which is indeed what the movie implies. But once people were cured, they would no longer be weak, and therefore should once again be "on the radar" of zombies, which would make the whole exercise pointless. Otherwise, if zombies could detect mere carriers of disease, anyone who'd ever had chicken pox ought to have been safe from zombie attack.

The only other option I can think of is cycles of giving people a disease, sending them out to kill zombies, giving them cures and then starting over with different diseases. That seems unsustainable, both for medical reasons and for running-out-of-available-diseases reasons, and also unsupported by the brief voiceover at the end of the movie. What am I missing here?