Combining Gompertzian growth and cell population dynamics

Frank Kozusko, Željko Bajzer

Research output: Contribution to journalArticlepeer-review

104 Scopus citations


A two-compartment model of cancer cells population dynamics proposed by Gyllenberg and Webb includes transition rates between proliferating and quiescent cells as non-specified functions of the total population, N. We define the net inter-compartmental transition rate function: φ(N). We assume that the total cell population follows the Gompertz growth model, as it is most often empirically found and derive φ(N). The Gyllenberg-Webb transition functions are shown to be characteristically related through φ(N). Effectively, this leads to a hybrid model for which we find the explicit analytical solutions for proliferating and quiescent cell populations, and the relations among model parameters. Several classes of solutions are examined. Our model predicts that the number of proliferating cells may increase along with the total number of cells, but the proliferating fraction appears to be a continuously decreasing function. The net transition rate of cells is shown to retain direction from the proliferating into the quiescent compartment. The death rate parameter for quiescent cell population is shown to be a factor in determining the proliferation level for a particular Gompertz growth curve.

Original languageEnglish (US)
Pages (from-to)153-167
Number of pages15
JournalMathematical Biosciences
Issue number2
StatePublished - Oct 2003


  • Cell kinetics
  • Gompertz growth model
  • Proliferation
  • Quiescence
  • Tumor growth

ASJC Scopus subject areas

  • Statistics and Probability
  • Modeling and Simulation
  • General Biochemistry, Genetics and Molecular Biology
  • General Immunology and Microbiology
  • General Agricultural and Biological Sciences
  • Applied Mathematics


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