Viruses from several different families are able to exploit their host's cell death programmes so as to maximize viral fitness. Consideration of the evolution of such strategies has lead to the suggestion that the virus should inhibit apoptosis, in order to prolong the life of the cell and thereby maximize the number of progeny virions. The host, on the other hand, should stimulate apoptosis thereby inhibiting viral growth and blocking viral spread. For example, the function of the latent membrane protein I (LMPI) of the Epstein-Barr virus and the bcl-2 homologue gene A179L of African swine fever virus is to inhibit apoptosis. However, in other cases it is the virus that stimulates cell death or the host that benefits from inhibiting apoptosis, such as in fatal alphavirus encephalitis. This has been explained by assuming that virus-induced apoptosis in non-regenerating cells would be detrimental to the host. We present a mathematical framework for understanding virus-induced apoptosis which accounts for these two opposite solutions to virus infection with respect to the mode of virus replication and the life cycle of the target cell.