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The lysogenic cycle is characterized by the integration of viral DNA into the host's genome, allowing the virus to remain in a dormant state for extended periods, sometimes even years. During this phase, the viral genetic material, or prophage, is copied along with the host cell's DNA every time the cell replicates. This means that the viral genes are passed on to daughter cells without immediately harming the host.

The correct response emphasizes this crucial aspect of the lysogenic cycle, distinguishing it from other viral replication methods, particularly the lytic cycle, where the host cell is rapidly destroyed. This integration aspect allows the virus to survive in the host without causing immediate damage, thereby maintaining a long-term relationship with the host cells.

Conversely, while other choices present potential aspects related to viral behavior, they do not accurately depict the lysogenic cycle's defining features. The immediate death of the host cell, rapid replication, and high mutation rates are more characteristic of the lytic cycle or general viral behavior but do not apply to the process of lysogeny itself. Understanding this cycle is critical for comprehending how certain viruses can persist undetected in a host and the implications this holds for viral diseases and treatments.