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系統識別號 U0002-1007201623091200
中文論文名稱 腫瘤模型的動態行為及其免疫治療
英文論文名稱 Dynamics of Tumor Models and Immunotherapy
校院名稱 淡江大學
系所名稱(中) 數學學系碩士班
系所名稱(英) Department of Mathematics
學年度 104
學期 2
出版年 105
研究生中文姓名 陳柏宇
研究生英文姓名 Po-Yu Chen
學號 601190175
學位類別 碩士
語文別 英文
口試日期 2016-06-13
論文頁數 17頁
口試委員 指導教授-楊定揮
委員-林建仲
委員-鄭凱仁
中文關鍵字 腫瘤模型  免疫療法 
英文關鍵字 Tumor model  Immunotherapy 
學科別分類 學科別自然科學數學
中文摘要 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。
英文摘要 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.
論文目次 Contents
1. Induction........................................1
2. Prelimary........................................4
3. Existence and Local Stability of Equilibria......9
4. Immunotherapy...................................11
5. Numerical Simulations and Discussion............12

List of Figures
1. The graphs of both side of equation(3.2)........11
2. Numerical simulation of solution of (1.1).......14
3. Numerical simulation of solution of (1.1).......14

List of tables
1. Parameter Values : units are in 1/day except
for g1, g2, g3, and b whose units are volume..13
參考文獻 Reference
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