Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells
In this work we present a mathematical model for tumor growth based on the biology of the cell cycle.For an appropriate description of the effects of phase-specific drugs, it is necessary to look at the cell cycle and itsphases. Our model reproduces the dynamics of three different tumor cell populat...
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| Format: | Article |
| Language: | English |
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AIMS Press
2012-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.241 |
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| author | Maria Vittoria Barbarossa Christina Kuttler Jonathan Zinsl |
| author_facet | Maria Vittoria Barbarossa Christina Kuttler Jonathan Zinsl |
| author_sort | Maria Vittoria Barbarossa |
| collection | DOAJ |
| description | In this work we present a mathematical model for tumor growth based on the biology of the cell cycle.For an appropriate description of the effects of phase-specific drugs, it is necessary to look at the cell cycle and itsphases. Our model reproduces the dynamics of three different tumor cell populations: quiescent cells,cells during the interphase and mitotic cells.Starting from a partial differential equations (PDEs) setting, a delay differential equations (DDE) model is derived for aneasier and more realistic approach.Our equations also include interactions of tumor cells with immune system effectors.We investigate the model both from the analytical and the numerical point of view, give conditions forpositivity of solutions and focus on the stability of the cancer-free equilibrium. Differentimmunotherapeutic strategies and their effects on the tumor growth are considered, as well. |
| format | Article |
| id | doaj-art-04c1773a21894f13aaea9055f928368c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2012-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-04c1773a21894f13aaea9055f928368c2025-01-24T02:05:29ZengAIMS PressMathematical Biosciences and Engineering1551-00182012-02-019224125710.3934/mbe.2012.9.241Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cellsMaria Vittoria Barbarossa0Christina Kuttler1Jonathan Zinsl2Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85748 Garching b. MünchenZentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85748 Garching b. MünchenZentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85748 Garching b. MünchenIn this work we present a mathematical model for tumor growth based on the biology of the cell cycle.For an appropriate description of the effects of phase-specific drugs, it is necessary to look at the cell cycle and itsphases. Our model reproduces the dynamics of three different tumor cell populations: quiescent cells,cells during the interphase and mitotic cells.Starting from a partial differential equations (PDEs) setting, a delay differential equations (DDE) model is derived for aneasier and more realistic approach.Our equations also include interactions of tumor cells with immune system effectors.We investigate the model both from the analytical and the numerical point of view, give conditions forpositivity of solutions and focus on the stability of the cancer-free equilibrium. Differentimmunotherapeutic strategies and their effects on the tumor growth are considered, as well.https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.241tumorcell cycle$g_1$$g_0$immunotherapy.chemotherapydelay differential equationsphase-specific drugsimmune system |
| spellingShingle | Maria Vittoria Barbarossa Christina Kuttler Jonathan Zinsl Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells Mathematical Biosciences and Engineering tumor cell cycle $g_1$ $g_0$ immunotherapy. chemotherapy delay differential equations phase-specific drugs immune system |
| title | Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells |
| title_full | Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells |
| title_fullStr | Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells |
| title_full_unstemmed | Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells |
| title_short | Delay equations modeling the effects of phase-specific drugs and immunotherapy on proliferating tumor cells |
| title_sort | delay equations modeling the effects of phase specific drugs and immunotherapy on proliferating tumor cells |
| topic | tumor cell cycle $g_1$ $g_0$ immunotherapy. chemotherapy delay differential equations phase-specific drugs immune system |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2012.9.241 |
| work_keys_str_mv | AT mariavittoriabarbarossa delayequationsmodelingtheeffectsofphasespecificdrugsandimmunotherapyonproliferatingtumorcells AT christinakuttler delayequationsmodelingtheeffectsofphasespecificdrugsandimmunotherapyonproliferatingtumorcells AT jonathanzinsl delayequationsmodelingtheeffectsofphasespecificdrugsandimmunotherapyonproliferatingtumorcells |