Mathematical models and dynamic behaviors of cancer treatment by continuous and pulsed radiotherapy
Mathematical models and dynamic behaviors of cancer treatment by continuous and pulsed radiotherapy
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DOI：
10.1007/s12190-022-01813-z
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发表时间：
2022-11-06
影响因子：
2.2
通讯作者：
Chen，Jing
中科院分区：
文献类型：
--
作者：
Liu，Zijian;Luo，Zhonghu;Chen，Jing
在这项研究中，两个数学模型介绍了描述治疗癌症的连续和脉冲放射治疗。在连续放疗模型中，我们确定了所有的平衡点，并进行了彻底的检查，这些平衡点的稳定性。提出了保证癌症被根除或与正常细胞达到正平衡的辐射剂量标准。在脉冲放射治疗模型中，得到了癌症存在周期解、癌症根除周期解和共存周期解的条件。同时，数值模拟了辐射剂量对肿瘤治愈和扩散的影响。一个简短的结论，以及一些有趣的主题进行了讨论。
In this study, two mathematical models are introduced to describe treatment of cancer by continuous and pulsed radiotherapy. In the continuous radiotherapy model, we determine all of the equilibrium points and conduct a thorough examination of the stability of these equilibria. Criterions of the radiation dose that guarantee the cancer to be eradicated or take a positive balance with normal cells are provided. In the pulsed radiotherapy model, conditions of the existence and stability of cancer win periodic solution, cancer eradication periodic solution and coexistent periodic solution are derived. Meanwhile, numerical simulations to the effect of radiation dose on the cure and spread of the cancer are carried out. A brief conclusion is presented, as well as a few intriguing subjects for additional investigation are discussed.