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Asymptotic Behavior of Cell Populations Described by Two-Type Reducible Age-Dependent Branching Processes With Non-Homogeneous Immigration

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  • OLLIVIER HYRIEN
  • NIKOLAY M. YANEV

Abstract

Stem and precursor cells play a critical role in tissue development, maintenance, and repair throughout the life. Often, experimental limitations prevent direct observation of the stem cell compartment, thereby posing substantial challenges to the analysis of such cellular systems. Two-type age-dependent branching processes with immigration are proposed to model populations of progenitor cells and their differentiated progenies. Immigration of cells into the pool of progenitor cells is formulated as a non-homogeneous Poisson process. The asymptotic behavior of the process is governed by the largest of two Malthusian parameters associated with embedded Bellman-Harris processes. Asymptotic approximations to the expectations of the total cell counts are improved by Markov compensators.

Suggested Citation

  • Ollivier Hyrien & Nikolay M. Yanev, 2012. "Asymptotic Behavior of Cell Populations Described by Two-Type Reducible Age-Dependent Branching Processes With Non-Homogeneous Immigration," Mathematical Population Studies, Taylor & Francis Journals, vol. 19(4), pages 164-176, October.
    • Handle: RePEc:taf:mpopst:v:19:y:2012:i:4:p:164-176
    DOI: 10.1080/08898480.2012.718934
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    References listed on IDEAS

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    1. Hyrien, Ollivier & Zand, Martin S., 2008. "A Mixture Model With Dependent Observations for the Analysis of CSFELabeling Experiments," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 222-239, March.
    2. Ollivier Hyrien & Margot Mayer-Pröschel & Mark Noble & Andrei Yakovlev, 2005. "A Stochastic Model to Analyze Clonal Data on Multi-Type Cell Populations," Biometrics, The International Biometric Society, vol. 61(1), pages 199-207, March.
    3. Yakovlev, A. & Yanev, N., 2007. "Age and residual lifetime distributions for branching processes," Statistics & Probability Letters, Elsevier, vol. 77(5), pages 503-513, March.
    4. Peter Jagers & Karin Harding, 2009. "Viability of Small Populations Experiencing Recurring Catastrophes," Mathematical Population Studies, Taylor & Francis Journals, vol. 16(3), pages 177-198.
    5. Kaplan, Norman & Pakes, A. G., 1974. "Supercritical age-dependent branching processes with immigration," Stochastic Processes and their Applications, Elsevier, vol. 2(4), pages 371-389, October.
    6. Nadia Lalam & Christine Jacob, 2007. "Bayesian Estimation for Quantification by Real-time Polymerase Chain Reaction Under a Branching Process Model of the DNA Molecules Amplification Process," Mathematical Population Studies, Taylor & Francis Journals, vol. 14(2), pages 111-129.
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    Cited by:

    1. Nina Daskalova, 2017. "Expectation maximization estimates of the offspring probabilities in a class of multitype branching processes with binary family trees," Mathematical Population Studies, Taylor & Francis Journals, vol. 24(4), pages 246-256, October.

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