Department of Biosystems Science and Engineering, ETH Zurich, Mattenstrasse, Basel, Switzerland.
Bull Math Biol. 2011 Aug;73(8):1881-908. doi: 10.1007/s11538-010-9596-2. Epub 2010 Nov 17.
RNA viruses exist in large intra-host populations which display great genotypic and phenotypic diversity. We analyze a model of viral competition between two viruses infecting a constantly replenished cell pool. We assume a trade-off between the ability of the virus to colonize new cells (cell killing rate or virulence) and its local competitiveness (replicative success within coinfected cells). We characterize the conditions that allow for viral spread by means of the basic reproductive number and show that a local coexistence equilibrium exists, which is asymptotically stable. At this equilibrium, the less virulent competitor has a reproductive advantage over the more virulent colonizer reflected by a larger equilibrium population size of the competitor. The equilibria at which one virus outcompetes the other one are unstable, i.e., a second virus is always able to permanently invade. We generalize the two-virus model to multiple viral strains, each displaying a different virulence. To account for the large phenotypic diversity in viral populations, we consider a continuous spectrum of virulences and present a continuum limit of this multiple viral strains model that describes the time evolution of an initial continuous distribution of virulence without mutations. We provide a proof of the existence of solutions of the model equations, analytically assess the properties of stationary solutions, and present numerical approximations of solutions for different initial distributions. Our simulations suggest that initial continuous distributions of virulence evolve toward a distribution that is extremely skewed in favor of competitors. At equilibrium, only the least virulent part of the population survives. The discrepancy of this finding in the continuum limit with the two-virus model is attributed to the skewed equilibrium subpopulation sizes and to the transition to a continuum. Consequently, in viral quasispecies with high virulence diversity, the model predicts collective virulence attenuation. This result may contribute to understanding virulence attenuation, which has been reported in several experimental studies.
RNA 病毒存在于宿主内的大型群体中，表现出巨大的基因型和表型多样性。我们分析了两种病毒感染不断补充的细胞池时的病毒竞争模型。我们假设病毒在新细胞中定植的能力（细胞杀伤率或毒力）与其局部竞争力（在共感染细胞中的复制成功）之间存在权衡。我们通过基本繁殖数来描述允许病毒传播的条件，并表明存在局部共存平衡，该平衡是渐近稳定的。在这个平衡点上，毒性较低的竞争者相对于毒性较高的殖民者具有繁殖优势，表现为竞争者的平衡种群大小更大。另一种病毒淘汰另一种病毒的平衡点是不稳定的，即第二种病毒总是能够永久入侵。我们将两病毒模型推广到多种具有不同毒性的病毒株。为了考虑病毒群体中巨大的表型多样性，我们考虑了连续的毒性谱，并提出了这种多病毒株模型的连续极限，该极限描述了在没有突变的情况下，初始连续的毒力分布的时间演化。我们提供了模型方程解的存在性证明，对定态解的性质进行了分析评估，并给出了不同初始分布下解的数值近似。我们的模拟表明，初始连续的毒力分布会朝着有利于竞争者的极度偏态分布演化。在平衡状态下，只有种群中最不毒的部分存活下来。这一发现与连续极限下的两病毒模型之间的差异归因于偏态平衡亚种群大小和向连续极限的转变。因此，在具有高毒性多样性的病毒准种中，该模型预测了集体毒性衰减。这一结果可能有助于理解毒力衰减，这在几项实验研究中都有报道。
