A virus that persists inside the host in an inactive resting state is called a Lysogenic state.
This Lysogenic state is an ability of a pathogenic virus to lie dormant within cells, which is also referred to as the Latency state of the viral life cycle.
They usually don't show any symptoms and will not replicate. They can last a long period of time before becoming active and causing symptoms.
When the person's immune system becomes impaired or weak then the virus becomes active and replicates uncontrollably which results in n severe symptoms. This phase is called the lytic phase of the viral life cycle.
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