Step 1: Understanding the Concept:
Post-exposure prophylaxis buys time. It only helps when the disease takes a while to actually appear after exposure, or when ready-made antibodies can be handed to the body straight away.
Step 2: Walk through the three diseases where it works.
Rabies has a long, slow incubation, so vaccine plus immunoglobulin after a bite reliably stops the disease. Hepatitis B also has a long incubation, so HBIG plus vaccine after exposure works well. Measles has an incubation of about 10 to 14 days, long enough for a vaccine given within 72 hours, or immunoglobulin within 6 days, to still help.
Step 3: Now test pertussis.
Pertussis comes on fast, within about a week to ten days of exposure. There simply is not enough time for a vaccine given after exposure to build protection, so contacts are instead covered with antibiotics such as azithromycin, not with a vaccine-based PEP.
Step 4: Final Answer:
Pertussis is the condition where post-exposure prophylaxis in the vaccine or immunoglobulin sense does not work.