Final answer:
Viruses establish a latent infection by integrating into the host genome.
Step-by-step explanation:
Viruses establish a latent infection by integrating into the host genome. When a virus integrates its genetic material into the DNA of the host cell, it becomes part of the host cell's genome. This allows the virus to remain dormant and hidden within the host cell, without causing immediate harm. Examples of viruses that establish latent infections include the herpes simplex virus and the human immunodeficiency virus (HIV).