Pet rodents are relatively (but not entirely) free of diseases that can pass to humans, but rodents kept in poor conditions by the breeder can easily pass disease amongst each other. When you buy a new animal, it is wise to ask if the breeder has a health guarantee, a period of time during which they will refund your money if the animal becomes ill or dies.
After the first couple of weeks, if your rodent is still healthy and happy (and you are not exposing it to new animals on a regular basis), you can feel more confident in its health. However, rodents are prone to tumors and respiratory illnesses as they age.
Because of their small size, it can be hard to save them – which is not to say that you shouldn’t try. Caught early, benign tumors can potentially be removed, and respiratory illnesses respond well to antibiotics, anti-inflammatories, or steroids.
Sadly, many rodents are good at disguising signs of illness, so by the time you notice, time is very short to intervene.