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

• 成果类型: Article
• 署名作者: Bansaye, Vincent
• 署名单位: Sorbonne Universite; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP465
• 发表日期: 2008
• 页码: 967-996
• 关键词: limit-theorems; markov-chains; extinction; BEHAVIOR; proofs

摘要

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