Stability of a stochastically perturbed model of intracellular single-stranded RNA virus replication

Compared to the replication of double-stranded RNA and DNA viruses, the replication of single-stranded viruses requires the production of a number of intermediate strands that serve as templates for the synthesis of genomic-sense strands. Two theoretical extreme mechanisms for replication for such single-stranded viruses have been proposed; one extreme being represented by the so-called linear stamping machine and the opposite extreme by the exponential growth. Of course, real systems are more complex and examples have been described in which a combination of such extreme mechanisms can also occur: a fraction of the produced progeny resulting from a stamping-machine type of replication that uses the parental genome as template, whereas other fraction of the progeny results from the replication of other progeny genomes. Martínez et al., Sardanyés et al. and Fornés et al. suggested and analyzed a deterministic model of single-stranded RNA (ssRNA) virus intracellular replication that incorporated variability in the replication mechanisms. To explore how stochasticity can affect this mixed-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.Leonid Shaikhet is supported by the Israel Science Foundation via grant No. 1128/14 and the Israeli Ministry of Absorption. Santiago F. Elena is supported by Spain's Ministerio de Economía, Industria y Competitividad grant BFU2015-65037-P and by Generalitat Valenciana grant PROMETEOII/2014/021. Andrei Korobeinikov is supported by the Spain's Ministerio de Economía, Industria y Competitividad grant MTM2015-71509-C2-1-R.Peer reviewe