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系統識別號 U0026-1207201810353900
論文名稱(中文) 登革熱疫情的數學建模及計算
論文名稱(英文) Mathematical Modeling and Computational Issues of Dengue Epidemic
校院名稱 成功大學
系所名稱(中) 數學系應用數學碩博士班
系所名稱(英) Department of Mathematics
學年度 106
學期 2
出版年 107
研究生(中文) 李昱勳
研究生(英文) Yu-Hsun Lee
學號 L16054075
學位類別 碩士
語文別 英文
論文頁數 20頁
口試委員 指導教授-舒宇宸
口試委員-陳旻宏
口試委員-劉育佑
中文關鍵字 登革熱  傳染病模型 
英文關鍵字 Dengue Fever  Epidemic Model 
學科別分類
中文摘要 2015 年,台南市爆發了嚴重的登革熱疫情。根據疫情的開放資料,我們發現了一些有趣的現象。我們使用 SEIR 模型並調整有效接觸率之參數,使其結果能與每日新增病例數吻合。藉由比較最佳化求出之有效接觸率及台南市政府所做之化學防治時間,我們發現有效接觸率之下降與政府防疫作為有正面相關。此外,我們比較了各區疫情的嚴重度,並找到了傳染趨勢與化學防治之間的關聯性。在未來,我們可以 整合多尺度方法與其他資料,如:地圖資料、社交資訊、天氣等,來建立異質資料 的多尺度傳染病模型。
英文摘要 Tainan experienced severe dengue epidemics in 2015. According to the open data, some interesting issues are found. We use Susceptible - Exposed - Infected - Recovered (SEIR) model and adjust the parameters in the effective contact rate to fit historical data. By comparing the trend of the optimized effective contact rate and the dates of the epidemic prevention works by the government, the decay after prevention works gives a positive evidence for those works of government. We also compare the severity of each districts, and the relationship between the trend of epidemics and the chemical prevention is found.
In the future, we will integrate the multi-scale method with different information, such as geographic map, social information, and climate to establish a multi-scale heterogeneous epidemic model and discuss its computational efficiency and related error analysis.
論文目次 摘要/Abstract i
誌謝 iii
List of Tables vi
List of Figures vii
1 Introduction 1
1.1 Motivation 1
1.2 Epidemic Model 2
1.2.1 SIR model 3
1.2.2 SEIR model 3
1.3 Basic Reproduction Number 5

2 Numerical Methods 7
2.1 Dormand–Prince method 7
2.2 Multi-scale method 8
2.3 Heterogeneous Data Processing 8
2.4 Optimization Process 10

3 Optimization Results 11
3.1 Large-scale region optimization 11
3.2 Small-scale regions optimization 13
3.3 Multi-scale regions optimization 16

4 Conclusion 17
References 18

A Mathematical Model Visualization System 19
A.1 Model Caculation 20
A.2 Data Visualization 20
參考文獻 [1] 臺南市行政區劃. https://commons.wikimedia.org/wiki/File:Tainan_map. png.
[2] 台南市政府. 104 年臺南市本土登革熱病例, 2015. http: //data.tainan.gov.tw/dataset/denguefevercases/resource/ 7617bfcd-20e2-4f8d-a83b-6f6b479367f9.
[3] W. O. Kermack and A. G. McKendrick. A Contribution to the Mathematical Theory of Epidemics. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 115(772):700–721, 1927.
[4] Adnan Khan, Muhammad Hassan, and Mudassar Imran. Estimating the basic reproduction number for single-strain dengue fever epidemics. Infectious Diseases of Poverty, 3(1):1–10, 2014.
[5] James Holland Jones. Notes on R0. Notes, pages 1–19, 2007.
[6] O Diekmann, J A P Heesterbeek, and Johan Metz. On the Definition and the Com- putation of the Basic Reproduction Ratio R0 in Models For Infectious-Diseases in Heterogeneous Populations. Journal of mathematical biology, 28:365–382, 1990.
[7] J.R. Dormand and P.J. Prince. A family of embedded Runge-Kutta formulae. Journal of Computational and Applied Mathematics, 6(1):19–26, mar 1980.
[8] WHO. Global Strategy for Dengue Prevention and Control 2012–2020. World Health Organiszation, page 43, 2012.
[9] 蘇慧貞. 氣候暖化對台灣防疫之風險與因應對策相關研究. Technical report, 2009.
[10] 台南市政府. 2015 年臺南市登革熱防疫作為. Technical report, 2015.
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