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A Host-Parasite Model for a Two-Type Cell Population

Part of: Special processes Markov processes Physiological, cellular and medical topics

Published online by Cambridge University Press:  04 January 2016

Gerold Alsmeyer  and
Sören Gröttrup
Gerold Alsmeyer*
Affiliation:
Westfälische Wilhelms-Universität Münster
Sören Gröttrup*
Affiliation:
Westfälische Wilhelms-Universität Münster
*
∗ Postal address: Institut für Mathematische Statistik, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, DE-48149 Münster, Germany.
∗ Postal address: Institut für Mathematische Statistik, Westfälische Wilhelms-Universität Münster, Einsteinstraße 62, DE-48149 Münster, Germany.
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Abstract

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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.

Keywords

Cell divisionbranching within branchingbranching process in a random environmenthost-parasite modelextinction characteristicslimit theorem

MSC classification

Primary: 60J85: Applications of branching processes 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60K37: Processes in random environments
Secondary: 92D25: Population dynamics (general) 92C37: Cell biology
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 45 , Issue 3 , September 2013 , pp. 719 - 741
Copyright
© Applied Probability Trust 

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