An infection with a latent virus is not a disease. See the following quotes from the NIH website:
"The terms "infection" and "disease" are not synonymous.
An infection results when a pathogen invades and begins growing within a host.
Disease results only if and when, as a consequence of the invasion and growth of a pathogen, tissue function is impaired."
"Acute viral infection associated with active replication and production of virions (presence of disease)
is very different from the persistent, latent and asymptomatic type of specific virus-host relationship (absence of disease).
In the latter case the virus genome is maintained in the host but no virions are produced for long periods of time
and no antiviral host immune response is elicited.
Small amounts of virions are produced episodically which is sufficient for transmission of the virus to new hosts.
Host switching involves changing over from an absence of disease in the latent host
to the reappearance of disease by reactivation in a different type of host.
This is the event that sometimes gives rise to an emergent viral disease."
Also consider the FDA:
"Some viruses, however, can enter a state known as latency in which the virus is not being replicated.
In the latent state, the virus does not cause disease."