When a child is bitten by a hamster, there is some chance of disease if the hamster has had plague or contact with other animals in the wild. Otherwise, the plague is usually not present.
Whether or not a child gets plague from a hamster bite depends on whether or not the hamster carries the plague bacteria. Yersinia pestis is the causative agent. If the hamster was purchased from the right source and has been kept at home with no contact with the outside environment, then the bite will not cause plague.
However, if the source of the hamster is unknown, or if it has been in contact with other animals in the wild, then the hamster may carry the plague bacteria, which has a certain probability of causing the disease, and it is recommended to consult a doctor in a timely manner, and be treated with streptomycin and other medications as prescribed by the doctor.
In short, the child was bitten by a hamster whether the plague need to be analyzed. Usually, it is unlikely that the bite of a domesticated hamster will cause plague.