Drug resistance is one of the most intractable issues to the targeted therapy for cancer diseases. To explore effective combination therapy schemes, we propose a mathematical model to study the effects of different treatment schemes on the dynamics of cancer cells. Then we characterize the dynamical behavior of the model by finding the equilibrium points and exploring their local stability. Lyapunov functions are constructed to investigate the global asymptotic stability of the model equilibria. Numerical simulations are carried out to verify the stability of equilibria and treatment outcomes using a set of collected model parameters and experimental data on murine colon carcinoma. Simulation results suggest that immunotherapy combined with chemotherapy contributes significantly to the control of tumor growth compared to monotherapy. Sensitivity analysis is performed to identify the importance of model parameters on the variations of model outcomes.

中文翻译：

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治疗肿瘤耐药性的联合疗法的数学模型

耐药性是癌症疾病靶向治疗最棘手的问题之一。为了探索有效的联合治疗方案，我们提出了一个数学模型来研究不同治疗方案对癌细胞动力学的影响。然后，我们通过寻找平衡点并探索其局部稳定性来表征模型的动态行为。构造李亚普诺夫函数来研究模型平衡的全局渐近稳定性。使用一组收集的模型参数和小鼠结肠癌实验数据进行数值模拟，以验证平衡和治疗结果的稳定性。模拟结果表明，与单一疗法相比，免疫疗法联合化疗对控制肿瘤生长有显着贡献。进行敏感性分析是为了确定模型参数对模型结果变化的重要性。