In Lai and Friedman (2017) partial differential equations are used to model an inhibition of tumor applying the therapy of cancer combined with cancer vaccine plus checkpoint immune inhibitors. It is assumed there that the tumor is a spherical model and the treatment by the vaccine and immune checkpoint is not mathematically optimized. In this article we do not assume the tumor has a spherical shape and we describe a dynamic programming method to derive a verification of $\epsilon$-optimality condition of the usage. We calculate numerically an $\epsilon$-optimal treatment.

中文翻译：

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抑制肿瘤的最佳控制，足够的新方法 $\epsilon$优化和数值计算

在Lai和Friedman（2017）中，偏微分方程被用来模拟结合癌症疫苗和检查点免疫抑制剂的癌症治疗对肿瘤的抑制作用。假定肿瘤是球形模型，并且疫苗和免疫检查点的治疗没有在数学上优化。在本文中，我们不假设肿瘤呈球形，而是描述了一种动态编程方法来得出对肿瘤的验证。$\epsilon$使用的最佳条件。我们通过数值计算$\epsilon$-最佳治疗。