Advances in Applied Probability

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

Gerold Alsmeyer and Sören Gröttrup

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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.

Article information

Adv. in Appl. Probab., Volume 45, Number 3 (2013), 719-741.

First available in Project Euclid: 30 August 2013

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Zentralblatt MATH identifier

Primary: 60J85: Applications of branching processes [See also 92Dxx] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K37: Processes in random environments
Secondary: 92D25: Population dynamics (general) 92C37: Cell biology

Cell division branching within branching branching process in a random environment host-parasite model extinction characteristics limit theorem


Alsmeyer, Gerold; Gröttrup, Sören. A host-parasite model for a two-type cell population. Adv. in Appl. Probab. 45 (2013), no. 3, 719--741. doi:10.1239/aap/1377868536.

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