针对癌症的化疗、免疫治疗和病毒治疗的数学模型
A Mathematical Model for Chemotherapy, Immunotherapy and Virotherapy Treatments of Cancer
AI总结：
本文提出一个结合化疗、免疫治疗和病毒治疗的癌症数学模型，通过计算机模拟展示联合治疗的效果，为优化治疗方案提供理论支持。
摘要：
我们继续研究Dutta等人2025年构建的癌症治疗模型，通过添加病毒治疗来扩展其中的化疗和免疫治疗。这是一个描述健康组织中癌症传播的动态系统模型。它允许对三种治疗方式的各种组合进行计算机实验，这些实验在实验室或实验中无法实现。创新点在于加入了病毒治疗。分析显示，模型解在每个有限时间区间内存在、有界且非负，因此在生物上是可行的。构建并实现了时间步进算法，并展示了计算机模拟。模拟显示了在不同治疗方案下疾病的发展情况，包括无治疗的基线案例、单独三种治疗的案例以及三种治疗的某些组合。这些模拟表明，联合治疗效果更佳。然而，我们未考虑三种治疗方式联合应用可能存在的限制或不兼容性，这在实践中可能存在问题。一旦在实际中得到验证，该模型可用于设计三种治疗方式的联合治疗方案以获得更好的疗效。
英文摘要：
We continue our study of a model for cancer treatment, constructed in Dutta et. al., 2025, by adding Virotherapy to the Chemotherapy and Immunotherapy studied there. It is a dynamical system model for the spread of cancer in healthy tissue. It allows computer experiments of various combinations of the three modalities, which cannot be performed in the laboratory or experimentally. The novelty is the addition of Virotherapy. The analysis shows that the model solutions exist, are bounded, and nonnegative on each finite time interval, thus biologically feasible. A time-stepping algorithm is constructed and implemented, and computer simulations are presented. The simulations show the development of the disease under various treatment options, including a baseline case without treatment, cases for each of the three treatments separately, and some combinations of the three treatments. These simulations indicate that combinations of treatments are more effective. However, we do not consider any limitation or incompatibilities of the joint application of the three modalities, that may exist in practice. Once validated in the field, the model can be used to design treatment schedules of combinations of the three modalities for improved outcomes.
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