Pets also carry certain bacteria, viruses, parasites, and fungi that can cause illness if transmitted to humans. Humans get these animal-borne diseases when they're bitten or scratched or have contact with an animal's waste, saliva, or dander.

These diseases can affect humans in many ways. They're of greatest concern to young children, infants, pregnant women, and people whose immune systems have been compromised by illness or disease. Infants and kids younger than 5 years old are at risk because their immune systems are still developing, and some infections that might make an adult just mildly sick can be more serious for them.
Healthy Family, Healthy Pets

But you don't have to give up your family's furry friends either. Pets can enrich your family life, and taking a few precautions can protect your kids from getting sick.

Protecting your family from pet-related infections begins before bringing a pet home. For instance, reptiles and amphibians should not be allowed as pets in any household with infants and young children.

Also consider the health and age of your kids before getting a pet. A pet that would require frequent handling is not recommended for any immunocompromised child (such as a child who has HIV, has cancer and is undergoing chemotherapy, or uses prednisone frequently). Kids with eczema should probably avoid aquariums.