STABILITY OF A STOCHASTICALLY PERTURBED MODEL OF INTRACELLULAR SINGLE-STRANDED RNA VIRUS REPLICATION

Abstract

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. 1 , Sardanyés et al. 2 and Fornés et al. 3 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.