Anti-angiogenesis therapy has been an emerging cancer treatment which may be further combined with chemotherapy to enhance overall survival of cancer patients. In this paper, we investigate a system of nonlinear ordinary differential equations describing a microenvironment consisting of host cells, tumor cells, immune cells and endothelial cells while incorporating treatment combination with chemotherapy and anti-angiogenesis therapy. We perform a dynamical systems analysis demonstrating that our model is able to capture the three phases of cancer immunoediting: elimination, equilibrium, and escape. In addition, we present transcritical bifurcations for relevant parameter values that correspond to the progression from the elimination phase to the equilibrium phase. A range of medically useful tumor doubling times were simulated to determine how combined therapy affects the tumor microenvironment over the course of a 250 day treatment. This analysis found two additional bifurcation parameters that move the system of equations from the equilibrium phase to the elimination phase. We determine that the most important aspect of an effective therapy is the activation of the anti-tumor immune response.

中文翻译：

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化疗与血管生成抑制剂联合治疗实体瘤

抗血管生成疗法已成为一种新兴的癌症治疗方法，可进一步与化学疗法相结合，以提高癌症患者的总体生存率。在本文中，我们研究了一个非线性常微分方程系统，该系统描述了由宿主细胞、肿瘤细胞、免疫细胞和内皮细胞组成的微环境，同时将治疗与化疗和抗血管生成治疗相结合。我们进行了动态系统分析，证明我们的模型能够捕捉癌症免疫编辑的三个阶段：消除、平衡和逃逸。此外，我们提出了相关参数值的跨临界分岔，这些参数值对应于从消除阶段到平衡阶段的进展。模拟了一系列医学上有用的肿瘤倍增时间，以确定联合治疗如何在 250 天的治疗过程中影响肿瘤微环境。该分析发现了两个额外的分岔参数，它们将方程组从平衡阶段移动到消除阶段。我们确定有效疗法最重要的方面是激活抗肿瘤免疫反应。