Yes it is contagious to only humans. The child did not get it from a cat. It's techical name so that you can look up info on the net is "Hand, foot and mouth disease"
Young children are primarily affected, but it may be seen in adults. Most cases occur in the summer and early fall. Outbreaks may occur among groups of children especially in child care centers or nursery schools. Symptoms usually appear 3 to 5 days after exposure.
Hand, foot, and mouth disease is usually spread through person-to-person contact
People can spread the disease when they are shedding the virus in their feces. It is also spread by the respiratory tract from mouth or respiratory secretions (such as from saliva on hands or toys). The virus has also been found in the fluid from the skin blisters. The infection is spread most easily during the acute phase/stage of illness when people are feeling ill, but the virus can be spread for several weeks after the onset of infection.
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Foot and Mouth virus 
Linear Mode
