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Steady States Analysis of a Nonlinear Age-Structured Tumor Cell Population Model with Quiescence and Bidirectional Transition

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Abstract

A nonlinear age-structured tumor cell population model with quiescence and bidirectional transition is presented and studied. The division rate of the proliferating cells is assumed to be nonlinear due to the limitation of the nutrient and space. The model includes a proportion of newborn cells that enter directly the quiescent phase with age zero. This proportion can reflect the effect of treatment by drugs such as erlotinib. The bidirectional transition between proliferating cells and quiescent cells is considered. The local and global stabilities of the trivial steady state are investigated. The existence and local stability of the positive steady state are also analyzed. Numerical simulations are performed to verify the results and to examine the impacts of parameters on the nonlinear dynamics of the model.

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Acknowledgements

This research was supported by the National Natural Science Foundation of China (11401060,11801047), the Basic and Advanced Research Project of Chongqing (cstc2016jcyjA0412), the Fundamental Research Funds for the Central Universities (ZYGX2016J131, ZYGX2016J138), the Program of Chongqing Innovation Team Project in University (CXTDX201601022) and Chongqing Municipal Education Commission (KJ1600522, KJ1705136, KJQN201900707).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, P.R. China

    Zijian Liu & Jin Yang

  2. School of Economics and Management, Beijing Jiaotong University, Beijing, 100044, P.R. China

    Chunfang Guo

  3. School of Mathematical Science, University of Electronic Science and Technology of China, Chengdu, 611731, P.R. China

    Hong Li

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  1. Zijian Liu
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Liu, Z., Guo, C., Yang, J. et al. Steady States Analysis of a Nonlinear Age-Structured Tumor Cell Population Model with Quiescence and Bidirectional Transition. Acta Appl Math 169, 455–474 (2020). https://doi.org/10.1007/s10440-019-00306-9

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  • DOI: https://doi.org/10.1007/s10440-019-00306-9

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