Final answer:
Isolation is necessary for 24 to 72 hours after the initiation of antibiotic therapy for a child with meningococcal meningitis.
Step-by-step explanation:
For a child with a diagnosis of meningococcal meningitis, the nurse would conclude that isolation is necessary for 24 to 72 hours after the initiation of antibiotic therapy. This is because meningococcal meningitis is caused by the bacteria Neisseria meningitidis, which can be spread from person to person through close contact. Isolation precautions are important during the early stages of treatment to prevent the spread of the disease to others.