脉冲输注寨卡的脑癌治疗模型的动力学分析
Dynamic Analysis of the Model of Brain Cancer Treatment by Pulse Infusion of Zika
DOI: 10.12677/AAM.2019.83050, PDF,    国家自然科学基金支持
作者: 李玉红, 刘 建：广州大学数学与信息科学学院，广东 广州
关键词: 脑癌；脉冲；稳定性；阈值；周期解；Brain Cancer； Pulse； Stability； Threshold； Periodic Solution
摘要: 本文利用生物数学建模的思想，构建了一个输注寨卡病毒的脑癌治疗数学模型。在没有脉冲输注的情形，得到了模型解的有界性和非负性，并且利用常微分方程稳定性理论分析了模型平衡点的稳定性和阈值 ；当考虑脉冲输注时，讨论了周期解的局部渐近稳定性，并对脉冲输注量进行了估计，最后通过数值模拟对文中的主要结论做了合理的解释。
Abstract: In this paper, we consider a bio-mathematical modeling to construct a pulse infusion of zika virus for the treatment of brain cancer. The boundedness and non-negativeness of the model are ob-tained. By means of the theory of pulse differential equation, we derive the stability and threshold of the equilibria of the model. Then, the asymptotic stability of the periodic solution under pulse condition is discussed. Finally, the pulse infusion volume of the model is estimated and numerical simulation is carried out.
文章引用：李玉红, 刘建. 脉冲输注寨卡的脑癌治疗模型的动力学分析[J]. 应用数学进展, 2019, 8(3): 439-454. https://doi.org/10.12677/AAM.2019.83050

参考文献

[1] Tian, J.P. (2011) The Replicability of Oncolytic Virus: Defining Conditions in Tumor Virotherapy. Mathematical Bio-sciences and Engineering, 8, 841-860. [Google Scholar] [CrossRef] [PubMed]
[2] Wodarz, D. (2001) Viruses as Antitumor Weapons. Cancer Research, 61, 3501-3507.
[3] Patel, M.R. and Kratzke, R.A. (2013) Oncolytic Virus Therapy for Cancer: The First Wave of Translational Clinical trials. Translational Research, 161, 355-364. [Google Scholar] [CrossRef] [PubMed]
[4] Dingli, D., Cascino, M.D., Josic, K., et al. (2006) Mathematical Modeling of Cancer Radiovirotherapy. Mathematical Biosciences, 199, 55-78. [Google Scholar] [CrossRef] [PubMed]
[5] 寨卡病毒或可治疗脑癌[J]. 中国肿瘤临床与康复, 2017, 24(11): 1394.
[6] Zhu, Z., Gorman, M.J., McKenzie, L.D., et al. (2017) Zika Virus Has Oncolytic Activity against Glioblas-toma Stem Cells. Journal of Experimental Medicine, 214, 2843-2857. [Google Scholar] [CrossRef] [PubMed]
[7] Zhou, L. (2013) The Clinical Research Progress for Oncolytic Ade-novirus Targeting Cancer Therapy. China Biotechnology, 33, 105-113.
[8] 王子子, 郭志明. 关于肿瘤溶瘤病毒疗法的数学模型及其分析[J]. 广州大学学报(自然科学版), 2017, 16(4): 14-26.
[9] LaSalle, J.P., 著, 陆征一, 译. 动力系统的稳定性[M]. 成都: 四川科学技术出版社, 2002.
[10] 张玉娟, 陈兰荪, 孙丽华. 一类具有脉冲效应的捕食者–食饵系统分析[J]. 大连理工大学学报, 2004(5): 769-774.
[11] 潘玉娜. 脉冲输注免疫因子的HIV治疗模型的动力学性质研究[D]: [硕士学位论文]. 衡阳: 南华大学, 2014.
[12] 曾广钊. 两次脉冲的微分方程数值模拟程序的设计[J]. 中山大学学报论丛, 2005(3): 131-133.

为你推荐