SIAM Journal on Applied Mathematics, Volume 80, Issue 2, Page 906-928, January 2020.
Melanoma, the deadliest form of skin cancer, is regularly treated by surgery in conjunction with a targeted therapy or immunotherapy. Dendritic cell therapy is an immunotherapy that capitalizes on the critical role dendritic cells play in shaping the immune response. We formulate a mathematical model employing ordinary differential and delay differential equations to understand the effectiveness of dendritic cell vaccines, accounting for cell trafficking with a blood and tumor compartment. We reduce our model to a system of ordinary differential equations. Both models are validated using experimental data from melanoma-induced mice. The simplicity of our reduced model allows for mathematical analysis and admits rich dynamics observed in a clinical setting, such as periodic solutions and bistability. We give thresholds for tumor elimination and existence. Bistability, in which the model outcomes are sensitive to the initial conditions, emphasizes a need for more aggressive treatment strategies, since the reproduction number below unity is no longer sufficient for elimination. A sensitivity analysis exhibits the parameters most significantly impacting the reproduction number, thereby suggesting the most efficacious treatments to use together with a dendritic cell vaccine.

中文翻译：

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通过树突状细胞治疗黑素瘤的隔室模型进行肿瘤控制，消除和逃逸

SIAM应用数学杂志，第80卷，第2期，第906-928页，2020年1月。
黑色素瘤是皮肤癌中最致命的形式，通常通过手术结合靶向疗法或免疫疗法进行治疗。树突状细胞疗法是一种利用树突状细胞在塑造免疫反应中发挥关键作用的免疫疗法。我们制定了一个数学模型，使用普通的微分方程式和延迟微分方程式来理解树突状细胞疫苗的有效性，并考虑了血液和肿瘤区室的细胞运输。我们将模型简化为一个常微分方程组。使用来自黑素瘤诱导的小鼠的实验数据验证了两种模型。我们简化模型的简单性允许进行数学分析，并允许在临床环境中观察到丰富的动力学，例如周期解和双稳态。我们给出了消除和存在肿瘤的阈值。模型结果对初始条件敏感的双稳态强调需要更积极的治疗策略，因为低于1的繁殖数量不再足以消除。敏感性分析显示出最显着影响繁殖数量的参数，从而建议与树突状细胞疫苗一起使用的最有效的治疗方法。