Open AccessBranching Stochastic Evolutionary Models of Cell Populations
Author(s) -
Ollivier Hyrien,
N. M. Yanev
Publication year - 2019
Publication title -
biomath communications
Language(s) - English
Resource type - Journals
eISSN - 2367-5241
pISSN - 2367-5233
DOI - 10.11145/bmc.2019.10.229
Subject(s) - poisson distribution , limiting , poisson process , branching process , stochastic modelling , population , branching (polymer chemistry) , biology , progenitor , stochastic process , progenitor cell , statistical physics , mathematics , stem cell , physics , genetics , sociology , statistics , chemistry , demography , engineering , mechanical engineering , organic chemistry
This review paper surveys results on branching stochastic models with and without immigration published during the past nine years. Studies of this class of stochastic models were motivated by the quantitative analysis of the dynamics of population of cells of the central nervous system, called the terminally differentiated oligodendrocytes, and their progenitor cells. We focus on original ideasspecifically developed for Sevastyanov branching processes allowing the contribution of an external cellular compartment (e.g., stem cells) via anonhomogeneous Poisson immigration process. Limiting distributions are discribed in the subcritical, critical and supercritical cases for various immigration rates.