Age-Dependent Branching Processes with Non-homogeneous Poisson Immigration as Models of Cell Kinetics

  • Ollivier HyrienEmail author
  • Nikolay M. Yanev


This article considers age-dependent branching processes with non-homogeneous Poisson immigration as models of cell proliferation kinetics. Asymptotic approximations for the expectation and variance–covariance functions of the process are developed. Estimators relying on the proposed asymptotic approximations are constructed, and their performance investigated using simulations.


Bellman–Harris branching process Renewal equation Quasi-likelihood Pseudo-likelihood Flow cytometry Leukemia Stem cells Oligodendrocytes 



The paper is supported by NIH R01 grant AI129518 (Hyrien) and grant KP-6-H22/3 from the NSF of the Ministry of Education and Science of Bulgaria.

This research is supported by NIH grants AI129518, NS039511, CA134839, and AI069351 (Hyrien) and grant KP6-H22/3 from the NSF of the Ministry of Education and Science of Bulgaria. The authors are grateful to their colleagues Drs. Mark Noble, Margot Mayer-Pröschel, and Craig Jordan for valuable discussions about the biological examples that motivated this work.


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© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Vaccine and Infectious Disease and Public Health Science DivisionsFred Hutchinson Cancer Research CenterSeattleUSA
  2. 2.Department of Probability and Statistics, Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria

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