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We consider a branching model introduced by Kimmel for cell division withparasite infection. Cells contain proliferating parasites which are sharedrandomly between the two daughter cells when they divide. We determine theprobability that the organism recovers, meaning that the asymptotic proportionof contaminated cells vanishes. We study the tree of contaminated cells, givethe asymptotic number of contaminated cells and the asymptotic proportions ofcontaminated cells with a given number of parasites. This depends on domainsinherited from the behavior of branching processes in random environment (BPRE)and given by the bivariate value of the means of parasite offsprings. In one ofthese domains, the convergence of proportions holds in probability, the limitis deterministic and given by the Yaglom quasistationary distribution.Moreover, we get an interpretation of the limit of the Q-process as thesize-biased quasistationary distribution.

Proliferating parasites in dividing cells: Kimmel’s branching model revisited