A host-parasite model for a two-type cell population

被引：3
作者：
Institut für Mathematische Statistik, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, DE-48149 Münster, Germany [1 ]
机构：
[1] Institut für Mathematische Statistik, Westfälische Wilhelms-Universität Münster, DE-48149 Münster
来源：
Adv Appl Probab | 2013年 / 3卷 / 719-741期
关键词：
Branching process in a random environment; Branching within branching; Cell division; Extinction characteristics; Host-parasite model; Limit theorem;
D O I：
10.1239/aap/1377868536
中图分类号：
学科分类号：
摘要：
We consider a host-parasite model for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a B-cell always splits into two cells of the same type, the two daughter cells of an A-cell can be of any type. The random mechanism that describes how parasites within a cell multiply and are then shared into the daughter cells is allowed to depend on the hosting mother cell as well as its daughter cells. Focusing on the subpopulation of A-cells and its parasites, our model differs from the single-type model recently studied by Bansaye (2008) in that the sharing mechanism may be biased towards one of the two types. Our main results are concerned with the nonextinctive case and provide information on the behavior, as n→∞, of the number of A-parasites in generation n and the relative proportion of A- and B-cells in this generation which host a given number of parasites. As in Bansaye (2008), proofs will make use of a so-called random cell line which, when conditioned to be of type A, behaves like a branching process in a random environment. © ?Applied Probability Trust 2013.
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页码：719 / 741
页数：22
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