Lysogenic infection is found in bacteriophages (viruses that attack bacteria).
In lysogenic infection the virus enters the bacteria, in which the phage cell integrates its DNA inside the host genome to produce prophage DNA.
Hence, it is characterized by the retention of the phage DNA molecules in the host bacterium, potentially for several thousands of cell divisions.
The method of insertion of DNA is similar to the episomal insertion of DNA (integration of plasmid DNA).
The bacteria host with the prophage remains dormant for multiple cell divisions, while the lysogen (bacterium) carrying prophage is typically indistinguishable physiologically from uninfected cells.
Gradually the prophage is released from the host genome and the phage reverts to the lytic mode (assembly of many phage cells in single bacteria), lysing the cell.