Hi,
Definitely some infections are transmitted from pets to humans, but not in the range of 70-80%. As far as viral infections are concerned, the most common one that is transmitted is rabies. It gets transmitted from an infected pet if it bites a human. The viruses of cold and cough are usually species specific. That means a virius infecting dos will not be transferred to other species. Same goes for cats and birds etc. It has also be seen that chronic streptcoccal infection (usually in prolonged sore throats) can be transmitted from pets to humans.
For more information on the dieses transmitted to humans from pets read here
http://www.kidshealth.org/parent/infections/skin/pet_infections.htmlI would advise you not to get panicky. The repeated colds can be due to some other cause also. You can try keeping your grandchild away from the pets for a month and observe. If the rate of cold infection goes down then it is definitely due to infection from the pets.
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Regards
Dr. Gupta