A hostparasite model for a twotype cell population
Abstract
A hostparasite model is considered for a population of cells that can be of two types, A or B, and exhibits unilateral reproduction: while a Bcell always splits into two cells of the same type, the two daughter cells of an Acell 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 Acells and its parasites, the model differs from the singletype model recently studied by Bansaye (2008) in that the sharing mechanism may be biased towards one of the two types. Main results are concerned with the nonextinctive case and provide information on the behavior, as $n\to\infty$, of the number Aparasites in generation n and the relative proportion of A and Bcells in this generation which host a given number of parasites. As in (Bansaye,2008), proofs will make use of a socalled random cell line which, when conditioned to be of type A, behaves like a branching process in random environment.
 Publication:

arXiv eprints
 Pub Date:
 April 2012
 arXiv:
 arXiv:1204.0401
 Bibcode:
 2012arXiv1204.0401A
 Keywords:

 Mathematics  Probability;
 60J85 (Primary) 60J80;
 60K37;
 92D25 (Secondary)
 EPrint:
 To appear in Advances in Applied Probability, Typos corrected