September 2013 A host-parasite model for a two-type cell population
Gerold Alsmeyer, Sören Gröttrup
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Adv. in Appl. Probab. 45(3): 719-741 (September 2013). DOI: 10.1239/aap/1377868536

Abstract

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.

Citation

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Gerold Alsmeyer. Sören Gröttrup. "A host-parasite model for a two-type cell population." Adv. in Appl. Probab. 45 (3) 719 - 741, September 2013. https://doi.org/10.1239/aap/1377868536

Information

Published: September 2013
First available in Project Euclid: 30 August 2013

zbMATH: 1305.92050
MathSciNet: MR3102469
Digital Object Identifier: 10.1239/aap/1377868536

Subjects:
Primary: 60J80 , 60J85 , 60K37
Secondary: 92C37 , 92D25

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

Rights: Copyright © 2013 Applied Probability Trust

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Vol.45 • No. 3 • September 2013
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