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.

中文翻译：

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细胞内单链 RNA 病毒复制的随机扰动模型的稳定性

与双链 RNA 和 DNA 病毒的复制相比，单链病毒的复制需要产生许多中间链，作为合成基因组正义链的模板。已经提出了这种单链病毒复制的两种理论上的极端机制；一个极端以所谓的直线冲压机为代表，另一个极端以指数增长为代表。当然，实际系统更复杂，并且已经描述了一些例子，其中也可能发生这种极端机制的组合：产生的后代的一小部分来自使用亲本基因组作为模板的冲压机类型的复制，而其他后代的一部分来自其他后代基因组的复制。马丁内斯等人。1, Sardanyés 等人。2和 Fornés 等人。3提出并分析了单链 RNA (ssRNA) 病毒细胞内复制的确定性模型，该模型在复制机制中包含可变性。为了探索随机性如何影响这种混合模型的主要特性，在本文中，我们考虑了随机扰动的稳定性细胞内 ssRNA 病毒复制的模型。使用直接李雅普诺夫方法，我们找到了该模型平衡状态概率稳定性的充分条件。这一结果证实，这种单链 RNA 病毒复制的异质模型对于环境的随机扰动是稳定的。