论文标题
细胞分裂下病毒种群的两个级分支模型
Two level branching model for virus population under cell division
论文作者
论文摘要
在本文中，我们研究了细胞分裂下病毒群体的两级分支模型。我们假设这些细胞携带病毒群体，这些病毒群体会随着竞争而演变为分支粒子系统，而细胞根据Yule过程分裂，从而将其病毒群体分为两个独立发展的亚种群。 然后，我们假设病毒种群的尺寸很大，并且将快速分支速率和巨大的种群密度极限描述为解决方案良好的马丁纳尔问题的解决方案。虽然验证紧密度是非常标准的，但我们为结论唯一性提供了feynman-kac二元性关系。此外，二元性关系允许进一步研究模型的长期行为。
In this paper we study a two-level branching model for virus populations under cell division. We assume that the cells are carrying virus populations which evolve as a branching particle system with competition, while the cells split according to a Yule process thereby dividing their virus populations into two independently evolving sub-populations. We then assume that sizes of the virus populations are huge and characterize the fast branching rate and huge population density limit as the solution of a well-posed martingale problem. While verifying tightness is quite standard, we provide a Feynman-Kac duality relation to conclude uniqueness. Moreover, the duality relation allows for a further study of the long term behavior of the model.
