臺灣博碩士論文加值系統

為了建構出一個專用來探索在腸病毒症候群中，具有最高的併發重症率與致死率的71型的傳染病數學模型，本文參考四個傳統的傳染病數學模型，以及在SARS流行期間用來預測疫情的兩個數學模型SEIJR和SIJR，並依據腸病毒71型的機理；建構出一個非線性的微分方程組，此數學模型在本文中暫被稱為SICR。
我們藉由SICR的解來模擬腸病毒疫情的發展，再從中尋覓控制疫情的良策；經分析模型中各參數對疫情的演化影響，發現病患隔離參數在疫情控制上扮演著最重要的角色，如範例所示。文中所呈現的SICR數學模型與一些數值實驗結果，可提供一些因應措施，作為幾乎是年年流行且年年變種的腸病毒症候群的防治參考。
截至目前為止，疫情數據仍相當欠缺，所以在僅能從公開資訊中整理估算疫情參數值的情況下；SICR模型數值實驗中僅能採用精準度偏低的參數值；以致模擬的精準度亦不高。欲改善此缺點仍有賴醫療資訊方面的協助。

In order to investigate enterovirus 71,which has the highest severe complications rate and the lethality in enterovirus syndrome, we tried to construct an epidemic model to explore possible preventions of the infectious disease. This paper refered to four traditional epidemic models and two epidemic models(SEIJR and SIR epidemic model) which were used to forecast the epidemic situation and construct a differential equation model according to the mechanism of enterovirus 71.This mathematical model was temporarily called SICR epidemic model in this paper.
After we simulated the development of epidemic situation with the solution of SICR epidemic model, we came up a good plan to control epidemic situation to analyze the parameter values of model that influenced epidemic situation evolved. We discovered the quarantining parameter was the most important factor to control epidemic situation, as shown in the examples. The SICR epidemic model and the result of experiment by numerical analysis may offer some preventions with reference to controlling epidemic situation of enterovirus syndrome.
Until now, we were still short of epidemic situation data, therefore we only could reorganize the estimate epidemic situation parameter value from the public information. The value of experiment in the SICR epidemic model could not only use the precise parameter value, but the precision in simulation. To improve this shortcoming, it was still necessary to depend on the assistance of the medical information.

誌謝 i
英文摘要 ii
中文摘要 iv
目次 v
圖目錄 vii
章節
第一章 緒論1
1.1　研究背景和動機 1
1.2 所需要處理的問題 2
第二章 腸病毒的流行病學概論 3
2.1　腸病毒的介紹 3
2.2 腸病毒併發重症 6
2.3 基本的預防動作 10
第三章 傳染病數學模型 12
3.1 傳染病數學模型 12
3.2 Si模型 12
3.3 SIS模型 16
3.4 SIR模型 22
3.5 SID模型 31
3.6 傳統模型的缺陷以及SEIJR模型和SIJR模型
33
第四章 SICR模型 38
4.1 建立新的理論模型 38
4.2 SICR模型的分析與討論 40
4.3 SICR模型的應用 54
4.4 隔離率的重要性 55
第五章 結論與展望 57
5.1 結論 57
5.2 展望 57
參考文獻. 59

一、中文文獻：
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(2004年11月).
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.138/wlxt/ncourse/mathlab/web/shiyan/front/StudyArea/word/state%2
0paper/2003/2003CMCMA-1-3.doc
[3] 王文昌，季節性時間序列資料預測的半參數迴歸模型，中國衛生
統計，14卷 第6期：第4-6頁，1997.
[4] 行政院衛生署疾病管制局官方網站：
http://www.cdc.gov.tw/mp.asp?mp=1
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download/%B8z%AFf%ACr%AD%AB%AFg%B1w%AA%CC%C1
%7B%A7%C9%B3B%B2z%BA%F5%ADn.doc
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刊，第41 期，2005年9月.
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applications/ ap_epidemic/index.html

二、英文文獻：
[1] Chowell G, Fenimore P W, Castillo-Garsow M A, et al. SARS
outbreak in Ontario, Hong Kong and Singapore: the role of diagnosis
and isolation as a control mechanism. Los Alamos Unclassified Report
LA-UR-03-2653(2003)
[2] Shujing Gao, Zhidong Teng, Juan J. Nieto, and Angela Torres,
Analysis of an SIR Epidemic Model with Pulse Vaccination
and Distributed Time Delay. Hindawi Publishing Corporation
Journal of Biomedicine and Biotechnology，Volume 2007, Article ID
64870, 10 pages.
[3] M. M. A. EL-Sheikh and S. A. A. EL-Marouf, On Stability and
Bifurcation of Solutions of an Seirepidemic Model with Vertical
Transmission. IJMMS 2004:56, 2971–2987, 31 October 2003.
[4] Helong Liu, Houbao Xu, Jingyuan Yu, and Guangtian Zhu,
Stability on Coupling SIR Epidemic Model with Vaccination.
Journal of Applied Mathematics 2005:4, (2005), 301–319.
[5] W. Piyawong, E. H. Twizell, A. B. Gumel, An Unconditionally
Covergent Finite-Difference Scheme for the SIR Model, Applied
Mathematics and Computation 146,(2003), 611-625.
[6] Guang Zhao Zeng, Lan Sun Chen, Li Hua Sun, Complexity of an SIR
Epidemic Dynamics Model with Impulsive Vaccination Control, Chaos,
Solitons and Fractals 26, (2005), 495-505.
[7] Natalia Carlson and Michelle Scott, Welcome to the World of
Picornavirus，http://www.stanford.edu/group/virus/picorna/2000/
picornavirus.html