The time before the symptoms of a viral infection appear is called the incubation period. During this time, viral genomes are replicating and the host is responding, producing cytokines such as interferon that can have global effects, leading to the classical symptoms of an acute infection (e.g., fever, malaise, aches, pains, and nausea). These symptoms are called the prodrome, to distinguish them from those characteristic of infection (e.g. paralysis for poliovirus, hemorrhagic fever for Ebolaviruses, rash for measles virus).
The incubation period of a viral infection
Source: Virology Blog