Cell contamination and branching process in random environment with immigration

Vincent Bansaye (1)

1 LPMA - Laboratoire de Probabilités et Modèles Aléatoires

We consider a branching model for a population of dividing cells infected by parasites. Each cell receives parasites by inheritance from its mother cell and independent contamination from outside the population. Parasites multiply randomly inside the cell and are shared randomly between the two daughter cells when the cell divides. The law of the number of parasites which contaminate a given cell depends only on whether the cell is already infected or not. We determine the asymptotic behavior of the number of parasites in a cell line, which follows a branching process in random environment with state dependent immigration. We then derive a law of large numbers for the asymptotic proportions of cells with a given number of parasites. The main tools are branching processes in random environment and laws of large numbers for Markov tree.

Mots clés: Branching processes in random environment with immigration (IBPRE). Markov chain indexed by a tree. Empirical measures. Renewal theorem.; Branching processes in random environment with immigration (IBPRE). Markov chain indexed by a tree. Empirical measures. Renewal theorem

Domaines: Probabilités [math.PR]

Vincent Bansaye. Cell contamination and branching process in random environment with immigration. 2009. ⟨hal-00278633v2⟩