A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponse
In this paper we use a mathematical model to study the effect ofan $M$-phase specific drug on the development of cancer, includingthe resting phase $G_0$ and the immune response. The cell cycle ofcancer cells is split into the mitotic phase (M-phase), thequiescent phase ($G_0$-phase) and the interph...
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| Language: | English |
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AIMS Press
2007-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.239 |
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| author | Wenxiang Liu Thomas Hillen H. I. Freedman |
| author_facet | Wenxiang Liu Thomas Hillen H. I. Freedman |
| author_sort | Wenxiang Liu |
| collection | DOAJ |
| description | In this paper we use a mathematical model to study the effect ofan $M$-phase specific drug on the development of cancer, includingthe resting phase $G_0$ and the immune response. The cell cycle ofcancer cells is split into the mitotic phase (M-phase), thequiescent phase ($G_0$-phase) and the interphase ($G_1,\ S,\G_2$ phases). We include a time delay for the passage through theinterphase, and we assume that the immune cells interact with allcancer cells. We study analytically and numerically the stabilityof the cancer-free equilibrium and its dependence on the modelparameters. We find that quiescent cells can escape the $M$-phasedrug. The dynamics of the $G_0$ phase dictates the dynamics ofcancer as a whole. Moreover, we find oscillations through a Hopfbifurcation. Finally, we use the model to discuss the efficiencyof cell synchronization before treatment (synchronization method). |
| format | Article |
| id | doaj-art-9d04c915034840d3aa3710a8f6c0c57c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-9d04c915034840d3aa3710a8f6c0c57c2025-01-24T01:53:27ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-01-014223925910.3934/mbe.2007.4.239A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponseWenxiang Liu0Thomas Hillen1H. I. Freedman2Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, T6G 2G1Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, T6G 2G1Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, T6G 2G1In this paper we use a mathematical model to study the effect ofan $M$-phase specific drug on the development of cancer, includingthe resting phase $G_0$ and the immune response. The cell cycle ofcancer cells is split into the mitotic phase (M-phase), thequiescent phase ($G_0$-phase) and the interphase ($G_1,\ S,\G_2$ phases). We include a time delay for the passage through theinterphase, and we assume that the immune cells interact with allcancer cells. We study analytically and numerically the stabilityof the cancer-free equilibrium and its dependence on the modelparameters. We find that quiescent cells can escape the $M$-phasedrug. The dynamics of the $G_0$ phase dictates the dynamics ofcancer as a whole. Moreover, we find oscillations through a Hopfbifurcation. Finally, we use the model to discuss the efficiencyof cell synchronization before treatment (synchronization method).https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.239hopf bifurcation.cancer growthcycle-phase-specific drugstime delay |
| spellingShingle | Wenxiang Liu Thomas Hillen H. I. Freedman A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponse Mathematical Biosciences and Engineering hopf bifurcation. cancer growth cycle-phase-specific drugs time delay |
| title | A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponse |
| title_full | A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponse |
| title_fullStr | A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponse |
| title_full_unstemmed | A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponse |
| title_short | A mathematical model for M-phase specific chemotherapy including the $G_0$-phase and immunoresponse |
| title_sort | mathematical model for m phase specific chemotherapy including the g 0 phase and immunoresponse |
| topic | hopf bifurcation. cancer growth cycle-phase-specific drugs time delay |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2007.4.239 |
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