腫瘤模型的動態行為及其免疫治療

Dynamics of Tumor Models and Immunotherapy

陳柏宇(Po-Yu Chen)

指導教授 ： 楊定揮

淡江大學/理學院/數學學系碩士班/碩士(2016年)

https://doi.org/10.6846/TKU.2016.00276

摘要

在這工作中，我們考慮KP腫瘤模型的動態系統。
首先，非負解是個別奠定無界性和有界性的解的充分條件，
然後我們呈現了在使用及不使用免疫療法的無腫瘤平衡解。
透過線性系統的局部分析，證明了無腫瘤平衡解的局部穩定性。
此外，也研究全域的動態結果。
接下來，我們找到正平衡解的存在性的充分條件，
不幸的是，還是有可能有其它正平衡解。
最後，我們有一些探討生物意義和數值模擬的結果。

關鍵字

腫瘤模型 ； 免疫療法

並列摘要

In this work, we consider the dynamics of KP tumor model [12]. First, the non-negativity of solutions are showed and sufficient conditions to guarantee the unboundedness and boundedness of solution are established, respectively. Then we present the explicit form of tumor-free equilibrium with or without treatment. By applying local analysis to the linearized system, local stability of the tumor free equilibrium are verified. Moreover, a global dynamical result is also investigated. Next, we find the sufficient condition of the existence of positive equilibria. Unfortunately, there maybe have other positive equilibria. Finally, some biological implications and numerical simulations are presented in the last section.

並列關鍵字

Tumor model ； Immunotherapy

參考文獻

[2] T. Boon and P. van der Bruggen. Human tumor antigens recognized by T lymphocytes. The Journal of experimental medicine, 183(3):725–729, 1996.

R. G. Fenton, L. Miller, M. Sznol, J. W. I. Smith, W. H. Sharfman, and D. L. Longo. Influence of Interleukin-2 Regimens on Circulating Populations of Lymphocytes After Adoptive Transfer of Anti-CD3-Stimulated T Cells:

[4] R. J. De Boer, P. Hogeweg, H. F. Dullens, R. A. De Weger, and W. Den Otter. Macrophage T lymphocyte interactions in the anti-tumor immune response: a mathematical model. Journal of immunology (Baltimore, Md. : 1950), 134(4):2748–2758, 1985.

[5] K. E. de Visser, A. Eichten, and L. M. Coussens. Paradoxical roles of the immune system during cancer development. Nature Reviews Cancer, 6(1): 24–37, 2006.

[6] C. DeLisi and A. Rescigno. Immune surveillance and neoplasia. I. A minimal mathematical model. Bull. Math. Biology, 39(2):201–221, 1977.