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Statistical Modeling for Biological Systems pp 21–46Cite as

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

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Abstract

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.

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Acknowledgements

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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Authors and Affiliations

  1. Vaccine and Infectious Disease and Public Health Science Divisions, Fred Hutchinson Cancer Research Center, Seattle, WA, USA

    Ollivier Hyrien

  2. Department of Probability and Statistics, Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Nikolay M. Yanev

Authors
  1. Ollivier Hyrien
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  2. Nikolay M. Yanev
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Correspondence to Ollivier Hyrien .

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Editors and Affiliations

  1. Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, NY, USA

    Anthony Almudevar

  2. Department of Biostatistics and Computational Biology, University of Rochester Medical Center, Rochester, NY, USA

    David Oakes

  3. Rochester, NY, USA

    Jack Hall

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Hyrien, O., Yanev, N.M. (2020). Age-Dependent Branching Processes with Non-homogeneous Poisson Immigration as Models of Cell Kinetics. In: Almudevar, A., Oakes, D., Hall, J. (eds) Statistical Modeling for Biological Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-34675-1_2

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