肿瘤传统与免疫治疗的混合动力系统研究

With the aging of the population, the destruction of the ecological environment, unhealthy lifestyles, food safety and other issues that led to the continued increase in the incidence of cancer, more and more attention has been paid to the combination of traditional therapy and immunotherapy. However, it is challenging to quantify and evaluate the effects of the implementation of time and effectiveness of traditional therapy, immunotherapy, bio-chemotherapy and human interventions on the treatment of cancer. Therefore, this project will take into account the surgery, radiotherapy, chemotherapy, immunotherapy, bio-chemotherapy and other treatment strategies, with the tumor density or number threshold being the basis for the implementation of treatment strategy, we construct a series novel hybrid tumor-immune dynamic models with feedback control. By taking advantages of the theoretical derivations, numerical simulations and optimization theory, the dynamics of hybrid systems are studied, and the theories of non-smooth dynamical system and the stochastic dynamical system and numerical simulations are developed. We study the effects of variable thresholds, the period, frequency and dosage of the applications of various treatment strategies on the successful control of tumor, and then determine the optimal period, frequency and dosage of the treatment so that the drug resistance can be reduced, all these results can provide quantitative basis for cancer treatment. It is of great theoretical and practical significance to design the optimal combination therapies for the treatment of cancer.

随着老龄化加剧、生态环境的破坏、不健康的生活方式及食品安全等问题导致癌症发病人数持续增高，传统的治疗与免疫疗法相结合的治疗策略越来越受到重视。但是如何同时量化和评估传统治疗、免疫疗法、生物化疗以及人为干预策略实施时间、有效性等对肿瘤治疗的影响，具有挑战性。因此，本项目将综合考虑手术、放化疗、免疫治疗以及生物化疗等治疗策略，以肿瘤密度或数量阈值作为治疗策略实施的依据，创新性地发展具有反馈控制的混合肿瘤-免疫动力学模型。采用理论分析、数值计算、最优化理论等方法和技巧，研究混合系统的动力学性质，发展非光滑动力系统、随机动力系统理论以及数值计算方法。分析动态的肿瘤细胞密度阈值、各种治疗策略实施的周期、频率、剂量等对成功控制肿瘤的影响，确定减弱肿瘤细胞抗药性的最佳生物化疗药物交替使用次数、剂量和频率，设计最优的组合治疗方案，为临床上治疗癌症提供决策的定量依据，具有重要的理论与现实意义。

本项目综合考虑手术、放化疗、免疫治疗以及生物化疗等治疗策略，以肿瘤密度或数量阈值作为治疗策略实施的依据，创新性地发展具有反馈控制的混合瘤免疫动力学模型。采用理论分析、数值计算、最优化理论等方法和技巧，研究混合系统的动力学性质，发展非光滑动力系统、随机动力系统理论以及数值计算方法。分析动态的肿瘤细胞密度阈值、各种治疗策略实施的周期、频率、剂量等对成功控制肿瘤的影响，确定减弱肿瘤细胞抗药性的最佳生物化疗药物交替使用次数、剂量和频率，设计最优的组合治疗方案，为临床上治疗癌症提供决策的定量依据，具有重要的理论与现实意义。. 本项目的研究已达到了预期目标，理论上丰富了脉冲动力系统和非光滑Filippov系统的研究方法，获得了一系列的研究成果，并在生物数学较高水平的国际杂志上发表。到目前为止，本项目在SCI源刊上共发表论文12篇。1名教师晋升为教授，3名硕士研究生毕业，16名硕士研究生在读。

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