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

TL;DR

This paper investigates the stability of a stochastic model of ssRNA virus replication within cells, demonstrating that the model remains stable under environmental stochastic perturbations using Lyapunov methods.

Contribution

It introduces a stochastic perturbation analysis of a deterministic ssRNA virus replication model, providing stability conditions in probability.

Findings

Model is stable under stochastic perturbations

Lyapunov method confirms stability conditions

Heterogeneous replication mechanisms are robust

Abstract

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.