  Replication of single-stranded RNA virus can be complicated, compared to that
of double-stranded virus, as it require production of intermediate antigenomic
strands that then serve as template for the genomic-sense strands. Moreover,
for ssRNA viruses, there is a variability of the molecular mechanism by which
genomic strands can be replicated. A combination of such mechanisms can also
occur: a fraction of the produced progeny may result from a stamping-machine
type of replication that uses the parental genome as template, whereas others
may result from the replication of progeny genomes. F. Mart\'{\i}nez et al. and
J. Sardany\'{e}s at al. suggested a deterministic ssRNA virus intracellular
replication model that allows for the variability in the replication
mechanisms.
  To explore how stochasticity can affect this model principal properties, in
this paper we consider the stability of a stochastically perturbed model of
ssRNA virus replication within a cell. Using the direct Lyapunov method, we
found sufficient conditions for the stability in probability of equilibrium
states for this model. This result confirms that this heterogeneous model of
single-stranded RNA virus replication is stable with respect to stochastic
perturbations of the environment.
