The type of infection you are referring to is called a lytic infection. In a lytic infection, the virus enters the host cell and takes over the cell's machinery for the sole purpose of replicating itself. This leads to the destruction of the host cell and the release of new viral particles, which can then go on to infect other cells. Lytic infections are typically associated with viruses that are known as lytic viruses, such as the influenza virus.
