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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 連豊力 | zh_TW |
| dc.contributor.advisor | Feng-Li Lian | en |
| dc.contributor.author | 李家瑞 | zh_TW |
| dc.contributor.author | Chia-Jui Lee | en |
| dc.date.accessioned | 2024-09-05T16:15:57Z | - |
| dc.date.available | 2024-09-06 | - |
| dc.date.copyright | 2024-09-05 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-08-15 | - |
| dc.identifier.citation | [1] WHO. "WHO COVID-19 dashboard data." https://data.who.int/dashboards/covid19/data (accessed.
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Watmough, "Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission," (in eng), Math Biosci, vol. 180, pp. 29-48, Nov-Dec 2002, doi: 10.1016/s0025-5564(02)00108-6. [20] A. I. Abioye et al., "Mathematical model of COVID-19 in Nigeria with optimal control," (in English), Results Phys., Article vol. 28, p. 10, Sep 2021, Art no. 104598, doi: 10.1016/j.rinp.2021.104598. [21] A. Atangana and S. I. Araz, "Mathematical model of COVID-19 spread in Turkey and South Africa: theory, methods, and applications," (in English), Adv. Differ. Equ., vol. 2020, no. 1, p. 89, Dec 2020, Art no. 659, doi: 10.1186/s13662-020-03095-w. [22] T. CDC. "傳染病統計資料查詢系統." https://nidss.cdc.gov.tw/nndss/disease?id=19CoV (accessed. [23] J. T. W. Suzanne Lenhart, Optimal Control Applied to Biological Models, 1st Edition ed. Chapman and Hall/CRC, 2007. [24] T. CDC. "疾管署嚴正澄清，依法採購及審查COVID-19疫苗，絕無外界質疑「一路開綠燈」情事." https://www.cdc.gov.tw/Bulletin/Detail/VaoxlYHF8imJH-Qj2851GA?typeid=9 (accessed. [25] MOHW. "網傳「政府採購快篩試劑較他國昂貴」絕非事實 切勿以訛傳訛." https://www.mohw.gov.tw/cp-17-69380-1.html (accessed. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/95342 | - |
| dc.description.abstract | 數學模型常被用來描述疾病傳播的動態。在這篇論文中，試圖找出一個最佳控制的方法來抑制COVID-19疾病的傳播，且擁有最佳的成本效益。首先提出一個數學模型來描述COVID-19傳播的人口動態。接著對模型實施數學分析，利用靈敏度分析找出模型中哪些參數對模型的影響較大。用非線性最小平方法對台灣2022年4月至6月的確診資料做擬合，估計並找出合適的模型參數。接下來將模型延伸至最佳控制問題，含有三個控制變數：個人保護、疫苗接種、快篩檢測。然後使用電腦軟體對加進控制變數的模型進行數值模擬。最後使用ICER方法分析各種控制政策的成本效益並找出成本效益最高的控制方法。 | zh_TW |
| dc.description.abstract | Mathematical model is widely used to describe the dynamics of disease transmission. In this thesis, we aim to find an optimal control method that mitigate the spread of the COVID-19 pandemic with the best cost-effectiveness. First, we propose a mathematical model to describe the population dynamics of the COVID-19 spread. We conduct mathematical analysis on the proposed model. We do sensitivity analysis to find out the parameters with stronger influence on the model using nonlinear least-squares fitting method with the data of COVID-19 confirmed cases in Taiwan from April to June, 2022 to estimate and obtain appropriate fitting parameters and model. Next, we extend the model to an optimal control problem by adding three control variables: personal protection, vaccination, and rapid test detection. After that, we do numerical simulation for the model with the implementation of control variables with software tools. Lastly, we evaluate the cost-effectiveness of each control strategy and determine the one with the best cost-effectiveness with the ICER method. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-09-05T16:15:57Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-09-05T16:15:57Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員會審定書 #
誌謝 i 摘要 ii ABSTRACT iii CONTENTS iv LIST OF FIGURES vi LIST OF TABLES viii Chapter 1 Introduction 1 1.1 Background 1 1.2 Motivation 2 1.3 Problem Formulation 2 1.4 Contribution 4 1.5 Organization of the Thesis 4 Chapter 2 Background and Literature Survey 5 2.1 Population Model for the COVID-19 Pandemic 5 2.2 Optimal Control 6 2.3 Cost-effectiveness Analysis 8 2.4 Flow Chart of the Research 9 Chapter 3 Formulation of Mathematical Model 10 3.1 Model Formulation 10 Chapter 4 Mathematical Analysis of Model 14 4.1 Positivity and Boundedness of Solutions 14 4.2 Disease-Free Equilibrium 16 4.3 Basic Reproduction Number 17 4.4 Endemic Equilibrium Point 19 4.5 Global Stability of Disease-free Equilibrium 20 4.6 Sensitivity Analysis 21 Chapter 5 Optimal Control of Mathematical Model 25 5.1 Formulation of Optimal Control Problem 25 5.2 Existence of Optimal Control 26 5.3 Pontryagin’s Maximum Principle 27 Chapter 6 Numerical Simulation 30 6.1 Parameter Estimation 30 6.2 Runge-Kutta 4th-order method 32 6.3 Forward-backward sweep method 33 6.4 Numerical Simulation of Optimal Control Problem 33 Chapter 7 Cost-effectiveness Analysis of Control 41 7.1 Incremental Cost-effectiveness ratio (ICER) 41 Chapter 8 Conclusion 51 REFERENCE 53 | - |
| dc.language.iso | en | - |
| dc.subject | COVID-19 | zh_TW |
| dc.subject | SEIR模型 | zh_TW |
| dc.subject | 基本傳染數 | zh_TW |
| dc.subject | 最佳控制 | zh_TW |
| dc.subject | 成本效益分析 | zh_TW |
| dc.subject | ICER | zh_TW |
| dc.subject | SEIR model | en |
| dc.subject | COVID-19 | en |
| dc.subject | ICER | en |
| dc.subject | cost-effectiveness analysis | en |
| dc.subject | basic reproduction number | en |
| dc.subject | optimal control | en |
| dc.title | COVID-19疫情模型的最佳控制與成本效益分析 | zh_TW |
| dc.title | Optimal Control and Cost-effectiveness Analysis for COVID-19 Pandemic Model | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 王富正;江明理 | zh_TW |
| dc.contributor.oralexamcommittee | Fu-Cheng Wang;Ming-Li Chiang | en |
| dc.subject.keyword | COVID-19,SEIR模型,基本傳染數,最佳控制,成本效益分析,ICER, | zh_TW |
| dc.subject.keyword | COVID-19,SEIR model,optimal control,basic reproduction number,cost-effectiveness analysis,ICER, | en |
| dc.relation.page | 54 | - |
| dc.identifier.doi | 10.6342/NTU202404223 | - |
| dc.rights.note | 未授權 | - |
| dc.date.accepted | 2024-08-15 | - |
| dc.contributor.author-college | 電機資訊學院 | - |
| dc.contributor.author-dept | 電機工程學系 | - |
| 顯示於系所單位： | 電機工程學系 | |
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