Final answer:
Erythema infectiosum (fifth disease), caused by parvovirus B19, does not require strict isolation once the rash appears. Other conditions like COVID-19 and mumps do.
Step-by-step explanation:
The condition that does not require strict isolation for a child who is hospitalized is erythema infectiosum (fifth disease), caused by parvovirus B19. Once the rash appears, the virus is less contagious and strict isolation is typically unnecessary. In contrast, conditions like COVID-19, mumps, and red measles are highly contagious and require strict isolation to prevent the spread of infection.