To incubate

[Justin Bieber]

When a bird, etc. incubates its eggs, it keeps them warm until the young come out, and when eggs incubate, they develop to the stage at which the young come out:

[Tanya Shivari]

When harmful bacteria or viruses incubate, or when a person or animal incubates them, they increase in size or number in the persons or animals body but do not yet produce the effects of disease.