Zentrum Mathematik, Technische Universitat Munchen, Munchen, Germany.
Math Biosci Eng. 2012 Apr;9(2):241-57. doi: 10.3934/mbe.2012.9.241.
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 its phases. 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 an easier 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 for positivity of solutions and focus on the stability of the cancer-free equilibrium. Different immunotherapeutic strategies and their effects on the tumor growth are considered, as well.
在这项工作中，我们基于细胞周期生物学提出了一个肿瘤生长的数学模型。为了对特定于相的药物的影响进行适当的描述，有必要研究细胞周期及其各阶段。我们的模型再现了三种不同的肿瘤细胞群体的动态：静止细胞、间期细胞和有丝分裂细胞。从偏微分方程（PDE）设置出发，推导出了延迟微分方程（DDE）模型，以便采用更简单、更现实的方法。我们的方程还包括肿瘤细胞与免疫系统效应物的相互作用。我们从分析和数值两个角度研究了该模型，给出了解的正定性条件，并关注无癌平衡点的稳定性。还考虑了不同的免疫治疗策略及其对肿瘤生长的影响。
