  RNA viruses exist in large intra-host populations which display great
genotypic and phenotypic diversity. We analyze a model of viral competition
between two different viral strains infecting a constantly replenished cell
pool, in which we assume a trade-off between the virus' colonization skills
(cell killing ability or virulence) and its local competition skills
(replication performance within coinfected cells). We characterize the
conditions that allow for viral spread by means of the basic reproductive
number and show that a local coexistence equilibrium exists, which is
asymptotically stable. At this equilibrium, the less virulent competitor has a
reproductive advantage over the more virulent colonizer. The equilibria at
which one strain outcompetes the other one are unstable, i.e., a second viral
strain is always able to permanently invade. One generalization of the model is
to consider multiple viral strains, each one displaying a different virulence.
However, to account for the large phenotypic diversity in viral populations, we
consider a continuous spectrum of virulences and present a continuum limit of
this multiple viral strains model that describes the time evolution of an
initial continuous distribution of virulence. We provide a proof of the
existence of solutions of the model's equations and present numerical
approximations of solutions for different initial distributions. Our
simulations suggest that initial continuous distributions of virulence evolve
towards a stationary distribution that is extremely skewed in favor of
competitors. Consequently, collective virulence attenuation takes place. This
finding may contribute to understanding the phenomenon of virulence
attenuation, which has been reported in previous experimental studies.
