Which process explains how viruses can become persistent in a host cell without killing it?

The process that explains how viruses can become persistent in a host cell without killing it is lysogenic replication. In lysogenic replication, the viral genome integrates into the host cell's DNA, forming what is known as a provirus. This allows the viral genetic material to be replicated along with the host's DNA during cell division, and the infected cell can continue to live and divide, passing the viral DNA to its daughter cells.

Unlike lytic replication, where the virus takes over the host cell's machinery to produce new virions and eventually causes cell lysis (death of the host cell), lysogenic replication is more of a passive infection. As a result, the host cell remains viable and can function normally, allowing the virus to persist without causing immediate harm.

Transduction and transformation are processes associated with horizontal gene transfer but are not primarily involved in the persistence of viruses within a host cell. These processes do not explain the viral latency seen in lysogenic replication. Therefore, lysogenic replication is key to understanding how certain viruses can establish long-term relationships with host cells without causing death.