Quasistationarity in a Branching Model of Division-Within-Division

  • Marek Kimmel
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 84)


Many biological processes include branching phenomena, which may be called division-within-division. Examples are gene amplification in cancer cells and elsewhere, plasmid dynamics in bacteria, and proliferation of viral particles in host cells. In some cases, the loss of “smaller” particles from the “large” ones leads to extinction of the latter. The logical question is then to ask about the distribution of the nonextinct particles, which mathematically leads to the consideration of quasistationarity, ie. stationarity of the process conditional on nonabsorption.

We consider a model in which the large particles follow a supercritical process, while the small ones divide subcritically. We demonstrate that the part of population of the large particles which contain at least 1 small particle may expand or decay, and that the distribution of the number of small particles in large particles tends to a limit. We also discuss biological significance of results of this type.


Small Particle Large Particle Gene Amplification Mouse Fibroblast Cell Line Quasistationary Distribution 
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Copyright information

© Springer Science+Business Media New York 1997

Authors and Affiliations

  • Marek Kimmel
    • 1
  1. 1.Department of StatisticsRice UniversityHoustonUSA

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