when does the genetic material of a host and a virus combine
Only when the host is infected by the virus.
Virus
When infected, a host cell is forced to rapidly produce thousands of identical copies of the original virus. 
wiki:11135454
Virus [SEP] Introduction
When infected, a host cell is forced to rapidly produce thousands of identical copies of the original virus. When not inside an infected cell or in the process of infecting a cell, viruses exist in the form of independent particles, or "virions", consisting of: (i) the genetic material, i.e., long molecules of DNA or RNA that encode the structure of the proteins by which the virus acts; (ii) a protein coat, the "capsid", which surrounds and protects the genetic material; and in some cases (iii) an outside envelope of lipids. The shapes of these virus particles range from simple helical and icosahedral forms to more complex structures.