臺灣博碩士論文加值系統

根據衛生署每年所公佈國人的十大死因，二十多年來，癌症一直高居國人十大死因首位。癌症是醫學術語，其為最常見的是惡性腫瘤，它的特性，除了不斷的成長及壓迫局部組織外，它還會發生轉移，因而無法根治，最後導致人的死亡。本研究透過一個腫瘤的數學模型(A mathematical model in tumor treatment)，利用Matlab的內建函數對數學模式做初步的數值積分，求出所有的均衡點，並將初始值資料輸入至此數學模式中，透過輸出之圖表，研究其最後的穩定狀態，分析腫瘤細胞最後是否會被消滅。

According to the Department of Health announced the top ten causes of death, cancer has been the top one in the past two decades. Cancer is the medical terminology and it’s usually shown as malignant tumor. In addition to its continuous growth and the oppression of local organizations, it also occurred to the transferring and finally led to the man''s death. This research calculates the solutions and all equilibrium points of the mathematical model. Input initial conditions to this mathematical model are found and analyzed to determine whether the tumor cells will be destroyed or not.

誌謝　…………………………………………………………………………………………i
中文摘要　………………………………………………………………………………ii
英文摘要　……………………………………………………………………………iii
目錄　………………………………………………………………………………………iv
圖目錄………………………………………………………………………………………iv
表目錄………………………………………………………………………………………iv
第一章 緒論………………………………………………………………………………1
第二章 數學模式　…………………………………………………………………4
第三章 均衡點分析…………………………………………………………………6
第四章 數值模擬與討　………………………………………………………10
第五章 參考文獻……………………………………………………………………15
附錄一　……………………………………………………………………………………16
附錄二　……………………………………………………………………………………18

圖目錄

圖4.1 數值模擬……………………………………………………………………10
圖4.2 數值模擬……………………………………………………………………11
圖4.3 數值模擬……………………………………………………………………12
圖4.4 數值模擬……………………………………………………………………13

表目錄

表一 數值分析………………………………………………………………………10
表二 數值分析………………………………………………………………………11
表三 數值分析………………………………………………………………………13
表四 數值分析………………………………………………………………………14

1.Denise Kirschner and John Carl Panetta (1998), Modeling
immunotherapy of the tumor–immune interaction, J. Math.
Biol., 37, 235-252.

2.Hsiu Chuan Wei (2010), On the bifurcation analysis of a
food web of four species, 215, 3280-3292.

3.A.Tsoularis (2001), Analysis of Logistic Growth Models,
Res. Lett. Inf. Math. Sci, 2, 23-46.

4.http://classes.entom.wsu.edu/543/functional.htm
5.http://www.smh.org.tw/mag1/001860.htm