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Mathematical Biosciences and Engineering

2007, Volume 4, Issue 2: 239-259. doi: 10.3934/mbe.2007.4.239
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A mathematical model for M-phase specific chemotherapy including the G0-phase and immunoresponse

  • 1.
    Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, T6G 2G1
  • 2.
    Department of Mathematical and Statistical Sciences, Centre for Mathematical Biology, University of Alberta, Edmonton, T6G 2G1
  • Received: 01 July 2006 Accepted: 29 June 2018 Published: 01 February 2007

  • MSC : 92B05.

  • In this paper we use a mathematical model to study the effect of an M-phase specific drug on the development of cancer, including the resting phase G0 and the immune response. The cell cycle of cancer cells is split into the mitotic phase (M-phase), the quiescent phase (G0-phase) and the interphase (G1, S, G2 phases). We include a time delay for the passage through the interphase, and we assume that the immune cells interact with all cancer cells. We study analytically and numerically the stability of the cancer-free equilibrium and its dependence on the model parameters. We find that quiescent cells can escape the M-phase drug. The dynamics of the G0 phase dictates the dynamics of cancer as a whole. Moreover, we find oscillations through a Hopf bifurcation. Finally, we use the model to discuss the efficiency of cell synchronization before treatment (synchronization method).

    Citation: Wenxiang Liu, Thomas Hillen, H. I. Freedman. A mathematical model for M-phase specific chemotherapy including the G0-phase and immunoresponse[J]. Mathematical Biosciences and Engineering, 2007, 4(2): 239-259. doi: 10.3934/mbe.2007.4.239

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  • In this paper we use a mathematical model to study the effect of an M-phase specific drug on the development of cancer, including the resting phase G0 and the immune response. The cell cycle of cancer cells is split into the mitotic phase (M-phase), the quiescent phase (G0-phase) and the interphase (G1, S, G2 phases). We include a time delay for the passage through the interphase, and we assume that the immune cells interact with all cancer cells. We study analytically and numerically the stability of the cancer-free equilibrium and its dependence on the model parameters. We find that quiescent cells can escape the M-phase drug. The dynamics of the G0 phase dictates the dynamics of cancer as a whole. Moreover, we find oscillations through a Hopf bifurcation. Finally, we use the model to discuss the efficiency of cell synchronization before treatment (synchronization method).


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