Final answer:
The route of transmission for the child's illness is most likely direct contact with saliva or respiratory secretions from an infected individual, possibly through a daycare setting where the virus can spread easily.
Step-by-step explanation:
The route of transmission for the illness in the 6-month-old girl is likely through direct contact with saliva or respiratory secretions. Considering she is attending daycare, where children are in close proximity, the virus could easily spread via droplets from sneezing or coughing.
Roseola infantum and Fifth disease are pediatric viral infections that are contagious and characterized by fever and rash. Roseola, usually caused by HHV-6, presents with high fever and a rash developing three to five days later, spreading from the trunk outward, sparing palms and soles. Fifth disease, caused by parvovirus B19, shows early cold-like symptoms and later a distinctive "slapped cheek" rash that then spreads to the body. The girl's symptoms resemble Roseola, marked by a dry cough, rhinorrhea, high fever, and spreading rash, potentially contracted at daycare or during travel.