  We study the population dynamics of lytic viruses which replicate slowly in
dividing host cells within an organism or cell culture, and find a range of
viral replication rates that allows viruses to persist, avoiding extinction of
host cells or dilution of viruses at too rapid or too slow viral replication.
For the within-host competition between multiple viral strains, a strain with a
"stable" replication rate could outcompete another strain with a higher or
lower replication rate, therefore natural selection of viruses stabilizes the
viral persistence. However, when strains with higher and lower than the
"stable" value replication rates are both present, competition between strains
does not result in dominance of one strain, but in their coexistence.
